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

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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.**

`GCF(-63xy^3; 9x^3y^3)=9xy^3`

`GCF(9xy^3;90x^2y^2)=9xy^2`

`GCF(9xy^2; 2x(8x^2+8x+5))=x`

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