How to factor a tri, quad, or polynomial.

Answers

Answer 1

Explanation:

Factoring to linear factors generally involves finding the roots of the polynomial.

The two rules that are taught in Algebra courses for finding real roots of polynomials are ...

Descartes' rule of signs: the number of positive real roots is equal to the number of coefficient sign changes when the polynomial is written in standard form.Rational root theorem: possible rational roots will have a numerator magnitude that is a divisor of the constant, and a denominator magnitude that is a divisor of the leading coefficient when the coefficients of the polynomial are rational. (Trial and error will narrow the selection.)

In general, it is a difficult problem to find irrational real factors, and even more difficult to find complex factors. The methods for finding complex factors are not generally taught in beginning Algebra courses, but may be taught in some numerical analysis courses.

Formulas exist for finding the roots of quadratic, cubic, and quartic polynomials. Above 2nd degree, they tend to be difficult to use, and may produce results that are less than easy to use. (The real roots of a cubic may be expressed in terms of cube roots of a complex number, for example.)

__

Personally, I find a graphing calculator to be exceptionally useful for finding real roots. A suitable calculator can find irrational roots to calculator precision, and can use that capability to find a pair of complex roots if there is only one such pair.

There are web apps that will find all roots of virtually any polynomial of interest.

_____

Additional comment

Some algebra courses teach iterative methods for finding real zeros. These can include secant methods, bisection, and Newton's method iteration. There are anomalous cases that make use of these methods somewhat difficult, but they generally can work well if an approximate root value can be found.


Related Questions

please help me
the denominator only

Answers

Answer:

6/51/33/1013/549/201/15

Step-by-step explanation:

You cannot subtract JUST a denominator. The subtraction sign is lower down because of the odd printing just like the equal signs.

1. The first thing you have to do is change this from a mixed fraction into an improper fraction in order to subtract. This becomes:

12/5 -6/5 (This is done by multiplying the large number by the denominator and adding it to the exsisiting numerator)12-6=6 therefore  the answer is 6/5

2. This one requires you to multiply your denominator so that it is the same for both fractions. The least common denominator (LCD) for these fractions is 12

7/12-1/4(3) (Because 3x4 is 12 which is the LCD)7/12-3/12 = 4/12 (this can be simplified)1/3

3. This is fairly straight-forward the denominators already match so just subtract the numerators

6/10-3/10= 3/10

4. Because we have a full number we must make it into a fraction in order to subtract it and also turn the mixed fraction into an improper fraction

We'll start with the mixed because we've done that before multiplying 4 by 5. Add to that 20 the 2 from the original fraction to get 22/ 5For the full number use the denominator of the number to determine the fraction. Multiply the full number by the denominator (5) to get 35 and place a 5 underneath and call it a day.Therefore: 35/5-22/5=13/5

5. This problem requires multiple steps the first would be to make improper fractions then get a LCD and then of course subtract.

(6x8)+2=48+2=50 --> 50/8(5x3)+4=15+4=19 --> 19/5LCD 5:5,15,20,25,30,40 & LCD 8: 8,16,24,32,40 LCD=40(50/8)x5-(19/5)x8 = 250/40-152/40 = 98/40 This can be simplified49/20

6. For this we will use another LCD.

LCD 3: 3,6,9,12,15 LCD 5: 5,10,15 LCD=15(2/3)x5-(3/5)x3 = 10/15-9/15 = 1/15

How does simple
interest show proportional reasoning and
relate to the percent equation?

Answers

Answer:

Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

Step-by-step explanation:

what is 24x + 4 = 52​

Answers

Answer:

x=2

Step-by-step explanation:

24x=48, x=2 (subtract 4 from both sides)

Answer:

[tex]\bf 24x+4=52[/tex]

[tex]\bf 24x+4-4=52-4[/tex]

[tex]\bf 24x=48[/tex]

[tex]\bf \cfrac{24x}{24}=\cfrac{48}{24}[/tex]

[tex]\boxed{\bf x=2}[/tex]

⊱ ────── {.⋅ ✯ ⋅.} ────── ⊰

How much money should Annika give Susan?

Answers

Answer:

it depends on how much Annika has and if she is willing to give Susan money

Step-by-step explanation:

I could have answered properly but i do not understand the question it just states that, look below

How much money should Annika give Susan?

plzzzz help me!!!



Plz don't steal my points or add a link​

Answers

Answer: What do you mean? if you till me i can help you

Step-by-step explanation:

m divided 6 when m=48

Answers

[tex]\dfrac m 6 = \dfrac{48}6 = \dfrac{ 8 \times 6}6 = 8[/tex]

whats the answer (10 points)

Answers

Answer:

x=79 degrees y=22degrees

Step-by-step explanation:

you see it has 2 equal sides, so the triangle is an isosceles triangle. If the triangle is isosceles, then its 2 base angles are equal, that is, x = 79 according to the triangle property, the 3 angles add up to 180 degrees, so you take 180 degrees minus 2 * 79 degrees you get a y angle equal to 22 degrees

PLEASE I NEED HELP!! Due TODAY!!!!! I need someone who is actually good at this!!

Answers

Answer:

#8= B

#6= C

#7= D

#9= C

#10= A

Step-by-step explanation:

[First one, aka #8] c

- subtract 7x from both sides

- divide by 5

- slope is m is y = mx + b

[Second one, aka #7] is d

- subtract 2x from both sides

- divide by 5

- find the negative reciprocal

[Third one, aka #6] is c

- will have a slope of 2 since it is parallel

- plug the point into y = 2x + b and solve for b

[Fourth one, aka #9] is a

- change in d over change in c

- 29 - 20 / 6 - 0 = 9/6 = 3/2

[Fifth one, aka #10] is b

- I created the system:

2h + m = 2.85

3h + 2m = 4.45

- Because he had two hotdogs (2h) and one milk (m), and then 3 hotdogs (3h) and 2 milk (2m) so option b matches the best

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Show that x^2-8x+20 can be written in the form (x-a)^2+a where a is an integer

Answers

Step-by-step explanation:

Let's complete the square

x²-8x=-20

x²-8x+(-4)²=-20+(-4)²

x²+(-4)²=-20+16

(x-4)²=-4

(x-4)²+4

where a is an integer as required

Diagram 5 shows a triangle ABD such that AD = 17 cm, AB = 10 cm and BD = 21 cm. The straight line AC is perpendicular to the straight line BD and the value of area of triangle ABD is an integer. Calculate the length of AC, in cm. (4 marks)​

Answers

Answer:

8

Step-by-step explanation:

100 = x^2 + AC^2

17^2 = AC^2 + (21 - x)^2

289 = AC^2 + 21^2 + x^2 - 2*21*x

289 = AC^2 + 441 + x^2 - 42x

from 1st equation AC^2 + x^2 = 100

289 = 441 + 100 - 42x

289 = 541 - 42x

42x = 541 - 289 = 252

x = 252/42 = 6

so AC^2 = 100 - 6^2 = 100 - 36 = 64

AC = 8

If the Diameter is 10 of a circle then what is the radius.

Answers

Answer:

5

Reasoning

[tex]Diameter=2*radius[/tex]

Answer:

5

Step-by-step explanation:

the radius is always half of the diameter

I really need help with this one it's due today!!

Answers

Answer:

-2/3

3/2

Step-by-step explanation:

So to have a line parallel the equation is: m1 = m2, meaning the slope (represented by m in this equation) is equal. So in the equation. 3y = - 2x + 4 you need to simplify the equation by dividing both sides by 3. Which would be like so: y = - 2/3x + 4/3, which the slope will be -2/3.

To be perpindicular you need the slope to be: m1 * m2 = - 1. So because we already know that the slope is -2/3, all we need to do is set up an equation: -2/3 * y = - 1

-2/3y = - 1

multiply both sides by 3/-2

y = 3/2

can someone help me with this work problem?
thank you!( ◜‿◝ )♡​

Answers

adddddddddddddddddddddddddddddddddddddddddddddddddddddd

-14 + -8/9 is equivalent to?

Answers

equal in force, amount, or value also : equal in area or volume but not superposable a square equivalent to a triangle. 2a : like in signification or import. b : having logical equivalence equivalent statements. 3 : corresponding or virtually identical especially in effect or function.

Translate the following phrase into an inequality:


"A number n minus 3.5 is less than or equal to 4."

PLEASE HELP I HAVE 6 MATH MISSING ASSIGNMENTS, I HATE HIGH SCHOOL

Answers

Answer:

The term "at least" means the lowest number you can have. In other words, you cannot have a number less than that point. So we use the greater than or equal symbol.

x - 3 ≥ - 5

Add 3 on both sides of the inequality.

x ≥ -2

x is any number greater than or equal to -2.

If the term was "at most", then that is the highest number you can have, and you can go no higher than that. In this case, we would have used the less than or equal to symbol.

These terms are important to understand when working with inequalities.

The value of the inequality form of the phrase "A number n minus 3.5 is less than or equal to 4." is (n - 3.5) ≤ 4 .

Used the concept of inequality that states,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given that;

The phrase is,

"A number n minus 3.5 is less than or equal to 4."

Now it can be written in inequality form as,

(n - 3.5) ≤ 4

Therefore, the inequality is,

(n - 3.5) ≤ 4

To learn more about inequality visit:

https://brainly.com/question/25944814

#SPJ3

What is the slope of the equation Y= 5/4 x - 7/4?

a. -7

b. -7/4

c. 5/4

d. 5

Answers

Answer:

a

Step-by-step explanation:

Answer: c

Step-by-step explanation:

The area of the pilgrims cornfield is 6,396 square feet. The width of the cornfield is 52 feed. What is the length of the cornfield? Show your work

Answers

Based on the area of the field and the width as well, the length is most likely 123 feet.

The area of the cornfield is calculated as:

= Length x Width

You have the width so you can substitute it in the equation to find the length:

6,396 = Length x 52

Solving would give:

Length = 6,396 / 52

= 123 feet

In conclusion, the length is 123 feet.

Find out more at https://brainly.com/question/20183786.

stteps for solving 6(4x-3) are shown

which of these is not a part of the solution prosess

Answers

Answer:2 4  −  1 8

Step-by-step explanation:

HELP WOULD BE APPRECIATED

Answers

Answer:

For the second one would be 36°

The mean test scores with standard deviations of four English classes are given below. Class Mean Standard Deviation Mrs. Jones 89 1. 9 Mrs. Rijo 82 1. 4 Mr. Phan 73 3. 4 Mrs. Scott 90 6. 1 Which statement is most likely to be true? The scores of Mrs. Scott’s class are the closest to the class mean. The scores of Mr. Phan’s class are the closest to the class mean. The scores of Mrs. Jones’s class are the closest to the class mean. The scores of Mrs. Rijo’s class are the closest to the class mean.

Answers

Answer:

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

The scores from Mrs. Rijo’s class are the closest to the class mean.

rewrite the expression as a single fraction 3/8 + 1/8

Answers

Answer:

Step-by-step explanation:

3/8+ 1/8 = 4/8

Im confused on this. Michael has some coins in his pocket consisting of dimes, nickels, and pennies. He has two more nickels than dimes, and three times as many pennies as nickels. How many of each kind of coin does he have if the total value is $0.52?

Answers

Answer:

Using a system of equations, it is found that he has 2 dimes, 5 nickels and 12 pennies.

In the system of equations, I am going to say that:

x is the number of dimes.

y is the number of nickels.

z is the number of pennies.

---------------------

Two more nickels than dimes, thus:

Three times as many pennies as nickels, thus:

---------------------

A dime is worth $0.1, a nickel is worth $0.05, and a penny is worth $0.01. Total of $0.52, thus:

Solving for x:

---------------------

Solving for y and z:

He has 2 dimes, 5 nickels and 12 pennies.

Someone tell me what this is plz

Answers

Answer:

This is an equilateral triangle, which means all the sides are equal.

Hence, all three angles are the same.

[tex]3x=\frac{180}{3}[/tex]

[tex]3x=60[/tex]

Therefore,

[tex]x=20[/tex]

Answer:

20

Step-by-step explanation:

3x+3x+60= 180

6x= 180-60

6x= 120

Shane is an a baseball team. He averages 6 hits in 30 times at bat. How many hits should you expect him to have after 180 times at bat

Answers

Answer = 36

30 x 6 = 180
6 x 6 = 36

Find the circumference of the
circle. Use 3.14 for it. Do not
round your answer.
C = [ ? ] feet
18 feet
Enter the number that
belongs in the green box.
Hint: C = 2tr

Answers

The answer is abc deft hi

please help me out yall!!​

Answers

Answer:

c

Step-by-step explanation:

The price of a cinnamon roll is $2.00. The bakery has a sale, and all prices are 10% off. What is the sale price of the cinnamon roll

Answers

Answer: $1.80

Step-by-step explanation:

10% is 1/10. To find 1/10 of $2 we must divide it by the bottom of the fraction and times the top. 200 divided by 10 is 20 cents, times that by 1 is still 20 so, 10% = 20 cents. To find the sale price, we must subtract the discount from the original price. $2 - 20 cents is $1.80.

Evaluate.
-|4ab- cl for a = -6, b = 3, and c = 2
A -74
B -70
C 70
74

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\boxed{\mathsf{-|4ab - c|}}\\\large\boxed{\mathsf{= - |4(-6)(3) - 2|}}\\\large\boxed{\mathsf{= -|(-24)(3) - 2|}}\\\large\boxed{\mathsf{= -|-72 - 2|}}\\\large\boxed{\mathsf{= - |-74|}}\\\large\boxed{\mathsf{= |-74|}}\\\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{Option\ A. -74}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\large\boxed{\heartsuit\ \frak{Amphitrite1040:)\ }\heartsuit}[/tex]

2. What is the exchange rate? Show your work. 1 US dollar = ___________ euro
help pls :(

Answers

Answer:

.88 Euro

Step-by-step explanation:

One U.S. dollar is equivalent to .88 Euro. Have a nice day!

Petra and Robyn work part-time on weekends. The ratio of Petra's wage to
Robyn’s is 4 : 3. If they earn $210 between them, how much does each of them take
home

Answers

Step-by-step explanation:

   4    +       3 = 7

petra   robyn    total

  210     /   7          =30

wage     total

              ratio

30× 4  = $120

     Petra's part

30× 3  =  $90

      Robyn’s part

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