Given the polynomial:
[tex]\[ -2ab + 5a^3b^2 \][/tex]
To factor this polynomial completely, we can follow these steps:
1. Identify the greatest common factor (GCF) of the terms. The terms are [tex]\(-2ab\)[/tex] and [tex]\(5a^3b^2\)[/tex].
2. The GCF of the coefficients [tex]\(-2\)[/tex] and [tex]\(5\)[/tex] is [tex]\(1\)[/tex], and the GCF of the variable parts is [tex]\(ab\)[/tex], as it's the highest power of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] that divides both terms.
Therefore, the GCF of the polynomial is [tex]\(ab\)[/tex].
3. Factor out the [tex]\(ab\)[/tex] from each term in the polynomial:
[tex]\[
-2ab + 5a^3b^2 = ab(-2 + 5a^2b)
\][/tex]
Thus, the complete factored form of the polynomial is:
[tex]\[
ab(5a^2b - 2)
\][/tex]
So, the factored form of the polynomial [tex]\(-2ab + 5a^3b^2\)[/tex] is:
[tex]\[
ab(5a^2b - 2)
\][/tex]
