Question

Hey! Can someone check my answers?

1.Find the greatest common factor: 20y^9 +5y^6
A. 5y^6
B. 5y^9
C. 10y^9
D. 20y^3

and

2. Find the greatest common factor: 12xy^5+ 60x^4y^2 _ 24x^3y#3.

A. 3x^4y^5
B. 6xy^5
C. 6xy^2
D. 12xy^2

Answer 1

The greatest common factor is the biggest number taken from the values.

Q1. The answer is A. 5y^6


`20 y^(9) +5 y^(6)= 4*5 y^(9)+5 y^(6)`
Since
`x^(a)* x^(b) =x^(a+b)`, then
`x^(9)= x^(3)* x^(6)`

Back to our expression:

`4*5 y^(9)+5 y^(6)=4*5 y^(3)*y^(6)+5 y^(6)=4 y^(3)*5y ^(6)+ 5y ^(6)*1=5 y^(6) (4y ^(3) +1)`
The greatest common factor is thus
`5 y^(6)`


Q2. The answer is D. 12xy^2


`12x y^(5)+60 x^(4) y^(2) -24 x^(3) y^(3)=12x y^(5)+5*12 x^(4) y^(2) -2*12 x^(3) y^(3)`
We will use the rule
`x^(a)* x^(b) =x^(a+b)` to factorise the exponents:

`12x y^(5)+5*12 x^(4) y^(2) -2*12 x^(3) y^(3)= \\ =12x*y^(2)*y^(3)+5*12*x* x^(3) *y^(2)-2*12x* x^(2) *y*y^(2)= \\ =12xy^(2)*y^(3)+12xy^(2)*5 x^(3) -12xy^(2)*2 x^(2) y= \\ =12xy^(2)(y^(3)+5 x^(3)-2 x^(2) y)`
The greatest common factor is thus
`12xy^(2)`