Question

Consider the function f(x)=x3+15x2+74x+120. If f(x)=0 for x=−6, for what other values of x is the function equal to 0? List the values separated by commas.

Answer 1

other x values are -5,-4

Explanation:

f(x)=0 for x=−6

Apply synthetic division to get the quotient . using that we find other two values of x

-6 1 15 74 120

0 -6 - 54 -120

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

1 9 20 0

the quotient is
`x^2+9x+20=0`

now factor the left hand side, product is 20 and sum is 9

`x^2+9x+20=0\\(x+5)(x+4)=0\\x+5=0 , x=-5\\x+4=0, x=-4`

So other x values are -5,-4