Question

Factor: 8x5 + 4x2 – 12

Answer 1

\(8x^5 + 4x^2 - 12\)?

Answer 2

Well, actually, if that's true, then
Hint: 8 + 4 - 12 = 0

Answer 3

Also, since we know x = 1, then x - 1 = 0 and x - 1 is a factor, therefore, we can split the polynomial in accordance with x - 1 as follows:
8x^5 + 4x^2 - 12 = 8x^5 - 8x^4 + 8x^4 - 8x^3 + 8x^3 - 8x^2 + 12x^2 - 12
= 8x^4(x - 1) + 8x^3(x - 1) + 8x^2(x - 1) + 12x(x - 1)
= (x - 1)(8x^4 + 8x^3 + 8x^2 + 12x)
= 4x(x - 1)(2x^3 + 2x^2 + 2x + 3)

Answer 4

Correction:
We know x = 1, then x - 1 = 0 and x - 1 is a factor, therefore, we can split the polynomial in accordance with x - 1 as follows:
8x^5 + 4x^2 - 12
= 8x^5 - 8x^4 + 8x^4 - 8x^3 + 8x^3 - 8x^2 + 12x^2 - 12x + 12x - 12
= 8x^4(x - 1) + 8x^3(x - 1) + 8x^2(x - 1) + 12x(x - 1) + 12(x - 1)
= (x - 1)(8x^4 + 8x^3 + 8x^2 + 12x + 12)
= 4x(x - 1)(2x^3 + 2x^2 + 2x + 3x + 3)

Answer 5

I wouldn't attempt to factor it beyond that

Answer 6

And there's another error in there. It's a typo. See if you can find it.