Question

Factorise:
x^4 - x^3 +8x - 8

Answer 1

I wish I was advanced in math.

Answer 2

For this polynomial, it'd best to separate it into two different polynomials, which are a lot easier to factor. We'll see that there's a common factor they share that we can use to simplify this equation.\[x^4-x^3+8x-8 = (x^4-x^3)+(8x-8)\] \[=x^3(x-1)+8(x-1)\]\[=(x-1)*(x^3+8)\] x^3-8 is an equation that we can see an obvious factor of without actually factoring -if we set it equal to 0, we can see that -2 is a cube root of -8, so we know that (x+2) is a factor! When we factor (x+2) out, we get:\[(x-1)(x+2)(x^2-2x+4)\] Now we're done! That quadratic isn't factorable.

Answer 3

Wow, that looks like a lot of work.

Answer 4

Thanks, can you also do it using the sum of the cubes formula? I don't really know your way..