factor out the greatest common factor. 7x^4-49x^3+14x^2=7x^2

yes

thanks for checking my work

To determine whether the expression, 7x^4 - 49x^3 + 14x^2 = 7x^2, is factored out correctly, we need to factor out the greatest common factor (GCF) from each term.

Step 1: Find the GCF of all the terms in the expression.
The GCF of 7x^4, -49x^3, and 14x^2 is 7x^2.

Step 2: Divide each term in the expression by the GCF.
When we divide 7x^4 by 7x^2, we get x^2.
When we divide -49x^3 by 7x^2, we get -7x.
When we divide 14x^2 by 7x^2, we get 2.

So, the factored expression becomes:
7x^4 - 49x^3 + 14x^2 = 7x^2 * (x^2 - 7x + 2)

Therefore, the given expression is not factored correctly as it should be 7x^2 * (x^2 - 7x + 2) rather than 7x^2.