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Factor the polynomial by its greatest common monomial factor.

14x^(2)+28x^(5)=

Factor the polynomial by its greatest common monomial factor. $\newline$ $14 x^{2}+28 x^{5}=$

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Factor sums and differences of cubes

Full solution

Q. Factor the polynomial by its greatest common monomial factor.

\newline

14 x^{2}+28 x^{5}=

Identifying the highest power of x: To find the greatest common monomial factor, we need to identify the highest power of $x$ that divides both terms and the largest number that divides both coefficients. $\newline$ The coefficients are $14$ and $28$ . The greatest common divisor (GCD) of $14$ and $28$ is $14$ . $\newline$ The variable parts are $x^2$ and $x^5$ . The greatest common factor in terms of $x$ is $x^2$ , since $x^2$ is the highest power of $x$ that divides both $x^2$ and $x^5$ .
Finding the greatest common divisor: Now, we divide each term by the greatest common monomial factor, which is $14x^2$ . $\newline$ $\frac{14x^2}{14x^2} = 1$ $\newline$ $\frac{28x^5}{14x^2} = 2x^3$
Determining the greatest common factor in terms of x: We can now write the original polynomial as the product of the greatest common monomial factor and the remaining terms. $\newline$ $14x^2 + 28x^5 = 14x^2(1 + 2x^3)$

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