Question

factor the following polynomial completely using the greatest common factor. if the expression cannot be factored, enter the expression as is. $36s^{8}t^{4}-42s^{5}t^{5}$

Explanation:

Step1: Find GCF of coefficients

Find GCF of 36 and 42. Prime - factorize: $36 = 2\times2\times3\times3$, $42=2\times3\times7$. GCF of 36 and 42 is $2\times3 = 6$.

Step2: Find GCF of variables

For $s$ terms, GCF of $s^{8}$ and $s^{5}$ is $s^{5}$ (using rule $a^{m}$ and $a^{n}$ with $m\geq n$, GCF is $a^{n}$). For $t$ terms, GCF of $t^{4}$ and $t^{5}$ is $t^{4}$. So GCF of variables is $s^{5}t^{4}$.

Step3: Factor out GCF

Factor out $6s^{5}t^{4}$ from $36s^{8}t^{4}-42s^{5}t^{5}$: $36s^{8}t^{4}-42s^{5}t^{5}=6s^{5}t^{4}(6s^{3}-7t)$.

Answer:

$6s^{5}t^{4}(6s^{3}-7t)$