Question

Show by factor theorem that (x+2) is a factor of x³+x²-4x-4

Answer 1

Answer

Yes it is the factor

Step by step explanation

The zero of x+2 is -2 [-2+2=0]

[p(x) = x³+x²-4x-4]

[p(-2) = (-2)^3+(-2)^2-4(-2)-4]

Solution

x³+x²-4x-4

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

-8+4+8-4

-12+12

=0

Hence, the remainder is zero which concludes that x+2 is the factor of x³+x²-4x-4

Answer 2

Answer:

(x+2) is a factor of x³+x²-4x-4

Step-by-step explanation:

Let $p(x)=x^{3} -x^{2} -4x-4$

By factor theorem, (x+2) is a factor of p(x) if p(-2) = 0

Therefore, It is sufficient to show that (x+2) is a factor of p(x).

Now, $p(x)=x^{3} +x^{2} -4x-4$

Therefore, $p(-2)=(-2)^{3} +(-2)^{2} -4*(-2)-4$

                            $=-8+4+8-4\\=0$

Therefore, (x+2) is a factor of $x^{3} +x^{2} -4x-4$

Hence, proved.