Question

question
factor completely.
$-40y^{4}z^{2} + 34x^{4}y^{7}$

Explanation:

Step1: Find the GCF of coefficients and variables

First, find the greatest common factor (GCF) of the coefficients \(-40\) and \(34\). The GCF of \(40\) and \(34\) is \(2\). For the variables, the common variable part is \(y^4\) (since \(y^4\) is the lowest power of \(y\) in both terms, and \(x^4\) only appears in the second term, \(z^2\) only in the first). So the GCF of the two terms is \(2y^4\). But we can also factor out a negative sign to make the leading coefficient positive, so we'll factor out \(-2y^4\) (or \(2y^4\), but factoring out \(-2y^4\) will make the first term inside the parentheses positive).

Step2: Factor out the GCF

Factor out \(-2y^4\) from \(-40y^4z^2 + 34x^4y^7\):

$$
LATEXBLOCK0
$$

We check if the expression inside the parentheses can be factored further. The terms \(20z^2\) and \(-17x^4y^3\) have no common factors (other than \(1\) or \(-1\)), so this is the complete factorization.

Answer:

\(-2y^4(20z^2 - 17x^4y^3)\)