Answer:
Step-by-step explanation:
If we look, "y" can be factored out of the entire expression because it goes into them all. This gives y(2x^3 - 4x^2 + 8x - 16)
Since everything inside the brackets is a multiple of 2 we can factor it out.
2y (x^3 - 2x^2 + 8x - 16)
Here to factor (x^3 - 2x^2 + 8x - 16) we could either use a calculator, or notice that when we subsitute 2 into the equation, it equals 0. Therefore (x - 2) must be a factor. The other factor must be (x^2 + 8) because:
(x - 2) ( )
We need to have 1 x^3 so we know the first part of the factor must be x^2
The also need to have -16 when we multiply this out, -2 * something equals -16. Meaning we must have 8 inside of the brackets.
This gives :
(x - 2) (x^2 + 8).
When we expand this out we get (x^3 - 2x^2 + 8x - 16)
Therefore in total we have
2y (x - 2)(x^2 + 8)
There are other methods of factorising (x^3 - 2x^2 + 8x - 16), so use the method which you have been taught in class or the one I used.
