Question

1) What is the GCF for the polynomial 4x3 - 2x2y?

2) What is the GCF for the polynomial 8x4y + 6x2y2?

3) What is the GCF for the polynomial 12x3y2 - 20x5y3?

4) What is the GCF for the polynomial -10x3y4 - 16x5y2?

Answer 1

1. 2x2

2. 2x2y

3. 4x3y2

4. -2x3y2

Explanation:

1. 4x3 - 2x2y= GCF: 2x2

2. 8x4y + 6x2y2= GCF: 2x2y

3. 12x3y2 - 20x5y3= GCF: 4x3y2

4. -10x3y4 - 16x5y2= GCF: -2x3y2

Answer 2

(1)the GCF for the polynomial
`4x^3 - 2x^2y`

4x^3 = 2*2* x* x* x

2x^2y = 2*x*x*y

Greatest common factor is
`2*x*x = 2x^2`

(2) the GCF for the polynomial
`8x^4y + 6x^2y^2`

`8x^4y = 2*2*2*x*x*x*x*y`

`6x^2y^2 = 3*2*x*x*y*y`

GCF is
`2*x*x*y=2x^2y`

(3) the GCF for the polynomial
`12x^3y^2 - 20x^5y^3`

`12x^3y^2 = 2*2*3*x*x*x*y*y`

`20x^5y^3=5*2*2*x*x*x*x*x*y*y*y`

GCF is
`2*2*x*x*x*y*y= 4x^3y^2`

(4) the GCF for the polynomial
`-10x^3y^4 - 16x^5y^2`

`-10x^3y^4 =-2*5*x*x*x*y*y*y*y`

`-16x^5y^2=-2*2*2*2*x*x*x*x*x*y*y`

GCF is
`-2*x*x*x*y*y= -2x^3y^2`