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Factor the GCF out of the polynomial below:

12x^(5)+4x^(3)+8x^(2)

Factor the GCF out of the polynomial below: $\newline$ $12 x^{5}+4 x^{3}+8 x^{2}$

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Multiply and divide rational expressions

Full solution

Q. Factor the GCF out of the polynomial below:

\newline

12 x^{5}+4 x^{3}+8 x^{2}

Identify Coefficients: First, let's look at the coefficients: $12$ , $4$ , and $8$ . The GCF of these numbers is $4$ .
Determine Variable Power: Now, let's look at the variables. The smallest power of $x$ in the terms is $x^{2}$ , so $x^{2}$ is part of the GCF.
Calculate GCF: So, the GCF of the polynomial is $4x^{2}$ . Now let's divide each term by $4x^{2}$ to factor it out.
Divide $12x^{5}$ : Dividing $12x^{5}$ by $4x^{2}$ gives us $3x^{3}$ .
Divide $4x^{3}$ : Dividing $4x^{3}$ by $4x^{2}$ gives us $x$ .
Divide $8x^{2}$ : Dividing $8x^{2}$ by $4x^{2}$ gives us $2$ .
Write Factored Form: Now, write the factored form of the polynomial: $4x^{2}(3x^{3}+x+2)$ .

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