Question

Is (x +1) a factor of f(x) = x^3 + x^2 −4x − 4?

Select the appropriate response:
Yes
or
No

Answer 1

Yes

Explanation:

( x^3 + x^2) (-4x - 4)

x^2 ( x+1) -4 (x+1)

(x^2 - 4) (x+1)

(x-2) (x+2) (x+1)

X= 2 x=-2 x=-1

Answer 2

Yes

Explanation:

f(x) = x^3 + x^2 −4x − 4

Factor by grouping taking x^2 out of the first group and -4 out of the second

0 = x^3 + x^2 −4x − 4

x^2(x+1) -4(x+1)

Factor out (x+1)

0=(x+1)(x^2-4)

Now we have the difference of squares

0=(x+1) (x-2)(x+2)

x+1 is a factor