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

S = 2πr² + 2πrhS = 2(3.14)(2)² + 2(3.14)(2)(3)S = 2(3.14)(4) + 2(3.14)(6)S = 2(12.56) + 2(18.84)S = 25.12 + 37.68S = 62.8...

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

katia87

12.07.2020

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)

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