Question

Use synthetic division and the given factor to completely factor the polynomial.

Answer 1

Hello there!


The factorization form is:

(x + 2)(x + 3)(x - 6)

I hope this helps!

Answer 2

Answer:

$f(x)=x^3-x^2-24x-36=(x-6)(x+3)(x+2)$      

Step-by-step explanation:

Given : $f(x)=x^3-x^2-24x-36$ ; (x-6)

To find : The complete factors of the polynomial using synthetic division.

Solution : To use synthetic division, start with the coefficients of the original polynomial, then put the 6 below it and off to the side:  

Now drop down the first 1, multiply it by the 6 and place it under the -1, then add the results. Then continue until the end. If you get 0, then (x - 6) is a factor and the numbers you end up with (minus the zero) are the coefficients of the quotient polynomial:

6 I 1______-1_______-24_____-36  

_ I 1______6_______ 30______36  

_ I 1______5_______ 6_______0  

Therefore, the resultant is $x^2 + 5x + 6$

Factor of $x^2 + 5x + 6$ by middle term split

$x^2 + 5x + 6$

$=x^2 + 3x +2x+ 6$

$=x(x+ 3)+2(x +3)$

$=(x+3)(x+2)$

So, The complete factors are $f(x)=x^3-x^2-24x-36=(x-6)(x+3)(x+2)$