How do I find the GCF of the four expressions i) -63XY^3 ii) 9X^3Y^3 iii) 90X^2Y^2 iv) 16X^3 + 16X^2 + 10X
A factor is a term that divides an expression exactly.
The gcf is the greatest common factor.
Let's start with the additive expression
`16x^3 + 16x^2 + 10x`
This factorises to
`2x(8x^2 + 8x + 5)`
The second part of this expression doesn't factorise (check with the quadratic formula that the roots aren't Real numbers).
Straightaway we can see that the first expression isn't divisible by 2 (in general - it may do if `x` is even or `y` is even). It is, however, divisible by `x`, as are all the other expressions. Discarding the final additive expression, the gcf of the first three is `9x` since `9 = gcf(-63,9,90)` and the lowest power in `x` is 1.
The gcf of the first three expressions is 9x. However, including the fourth additive expression, the gcf is x.