Question

How do I find the greatest common factor for this polynomial? I am having trouble understanding GCF.

Answer 1

Given

`24x^4y-9x^3y^3-12x^3y^2=0`

We are asked to find the GCF

Solution

How to Find a Greatest Common Factor in a Polynomial

1. Break down every term into prime factors. ...

2. Look for factors that appear in every single term to determine the GCF. ...

3. Factor the GCF out from every term in front of parentheses and group the remnants inside the parentheses. ...

`\begin{gathered} 24x^4y-9x^3y^3-12x^3y^2=0 \\ First,\text{ break the numbers to prime factor} \\ 2*2*2*3* x^4y-3*3* x^3y^3-2*2*3* x^3* y^2 \\ \end{gathered}`
`\begin{gathered} \text{second and third Look for the GC factors that appear single term} \\ 3x^3y(8x-3y^2-4y)=0 \end{gathered}`

The final answer

`\text{The GCF is 3}^{}x^3y`