Sure, let's factor the expression [tex]\(-26 x^5 y^3 + 44 x^2\)[/tex] step by step.
1. Identify the Greatest Common Factor (GCF) of the coefficients:
We look at the coefficients [tex]\(-26\)[/tex] and [tex]\(44\)[/tex]. The greatest common factor (GCF) of these two numbers is [tex]\(2\)[/tex].
2. Identify the common variable factor:
The given expression has the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. We need to find the lowest power of the variable [tex]\(x\)[/tex] that appears in both terms. In [tex]\(-26 x^5 y^3\)[/tex], the variable [tex]\(x\)[/tex] appears as [tex]\(x^5\)[/tex], and in [tex]\(44 x^2\)[/tex], it appears as [tex]\(x^2\)[/tex]. The lowest power of [tex]\(x\)[/tex] common to both terms is [tex]\(x^2\)[/tex].
3. Factor out the GCF and the common variable factor from each term:
The common factor that we can factor out from both terms is [tex]\(2 x^2\)[/tex].
4. Write the factored expression:
[tex]\[
-26 x^5 y^3 + 44 x^2 = 2 x^2 \left(\frac{-26 x^5 y^3}{2 x^2} + \frac{44 x^2}{2 x^2}\right)
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
-26 x^5 y^3 / 2 x^2 = -13 x^3 y^3
\][/tex]
and
[tex]\[
44 x^2 / 2 x^2 = 22
\][/tex]
5. Combine the results:
[tex]\[
-26 x^5 y^3 + 44 x^2 = 2 x^2 (-13 x^3 y^3 + 22)
\][/tex]
Therefore, the factored form of the expression [tex]\(-26 x^5 y^3 + 44 x^2\)[/tex] is:
[tex]\[
2 x^2 (-13 x^3 y^3 + 22)
\][/tex]
