Question

Which binomial is a factor of x4 − 4x2 − 4x 8?

Answer 1

The given polynomial is

$x^4-4x^2-4x-8$

As this is a fourth degree polynomial, we can not directly use any formula, So here we will use hit and trial method

check whether x=-1 is a zero of the polynomial or not

$(-1)^4-4(-1)^2-4(-1)-8=-7$

Hence x=-1 is not a zero.

Now check whether x=-2 is a zero of the polynomial or not

$(-2)^4-4(-2)^2-4(-2)-8=0$

Hence x=-2 is a zero of the polynomial.

Hence we can re-write the polynomial as

$x^4-4x^2-4x-8=x^4+2x^3-2x^3-4x^2-4x-8\\ \\ =x^3(x+2)-2x^2(x+2)-4(x+2)\\ \\ =(x+2)(x^3-2x^2-4)$

Hence the required binomial is (x+2)