Identify the GCF of 10x4y3 − 5x3y2 + 20x2y. 10x2y 10x3y 5x2 5x2y

The GCF, or greatest common factor, is the greatest positive integer that evenly multiplies to make the numbers in the set. For simple numbers, GCF(12, 80, 44) is 4.

The strategy for expressions with variables is still to factor out the greatest term.

For [tex]10x^4y^3-5x^3y^2+20x^2y[/tex], we look for the largest factor in each term.

For [tex]10x^4y^3[/tex], the largest factors are [tex]x^4[/tex] and [tex]y^3[/tex]. We'll come back to the coefficients in a minute.

For [tex]-5x^3y^2[/tex], the largest factors are [tex]x^3[/tex] and [tex]y^2[/tex]. Now, looking back to the previous term and also considering the coefficients, the largest factor of the two is [tex]5x^3y^2[/tex]. You could rewrite the first term as [tex](5x^3y^2)(2xy)[/tex] and the second term as [tex]-1(5x^3y^2)[/tex].

Now, we consider the last term, [tex]20x^2y[/tex]. The largest factor common to the two other terms is [tex]5x^2y[/tex].

And that's our final answer for the GCF (answer D).