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

Answer:

other x values are -5,-4

Step-by-step 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