Factor the expression 5a^2b^5+10ab-15ab^3

 Exercise

$5a^2b^5\:+10ab-15ab^3$

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Factor the polynomial $5a^2b^5+10ab-15ab^3$ by it's greatest common factor (GCF): $5ab$

$5ab\left(ab^{4}+2-3b^2\right)$

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Sort the polynomial $\left(ab^{4}+2-3b^2\right)$ in descending order to handle it more easily

$5ab\left(ab^{4}+2-3b^2\right)$

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Factor the trinomial $\left(ab^{4}+2-3b^2\right)$ finding two numbers that multiply to form $2$ and added form $-3$

$\begin{matrix}\left(-1\right)\left(-2\right)=2\\ \left(-1\right)+\left(-2\right)=-3\end{matrix}$

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Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

$5ab\left(a^{0.5}b^{2}-1\right)\left(a^{0.5}b^{2}-2\right)$

$5ab\left(a^{0.5}b^{2}-1\right)\left(a^{0.5}b^{2}-2\right)$

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