Question

Algebra 2 please help ASAP

Monica wants to find the GCF of the terms of the polynomial p(x)=12x^3y+6y^2+18xy+24x. She sees that each term is divisible by 3.She factors the polynomial as follows:3x(4x^2y+2y^2+6y+8
Did Monica correctly factor out the GFC? Why or why not?

Answer 1

No, Monica did not correctly factor out the GCF

Explanation:

The given expression is
`12x^3+6y^2+18xy+24x`

The prime factorization of each term are:

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

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

`18xy=2*3^2* x* y`

`24x=2^3*3* x`

The greatest common factor is the product of the least powers of the common factors.

`GCF=2*3=6`

The greatest common factor is 6.

If we factor the GCF, we obtain:

`6(2x^3+6y^2+3xy+4)`

Therefore Monica did not correctly factor out the GCF