# How do you factor given that #f(8)=0# and #f(x)=x^3-11x^2+14x+80#?

##### 1 Answer

#### Explanation:

Since

Divide the function by

How to perform polynomial division when the divisor is a binomial:

1. Treat each term of the dividend as a "digit". We will performing division by "digit" (similar to number division)

2. Perform division with the first "digit" of the binomial only

3. When multiplying the resulting quotient back with the divisor, include the remaining digit

4. Subtract the resulting product from the dividend

5. Repeat 1-4 with the resulting difference until division is no longer possible

I can't format the polynomial division properly so I will apologize in advance.

<pre>

x^2 - 3x - 10

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

x - 8 / x^3 - 11x^2 + 14x + 80

- (x^3 - 8x^2)

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

-3x^2 + 14x + 80

-(-3x^2 + 24x)

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

-10x + 80

-10x + 80

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

0

</pre>

Factor out the quadratic polynomial

List out all the factors of the last term

We need the product to be negative, the factors need to be of different sign.

Take a look at the sign of the middle term

Add the factors, the resulting value should be equal to the middle term