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Which expression is the result of factoring the expression below by taking out its greatest common factor?

10x^(2)+50 x=?
Choose 1 answer:
(A)
10 x(x^(2)+5x)
(B)
x(10x^(2)+50 x)
(C)
10 x(x+5)
(D)
x(10 x+50)

Which expression is the result of factoring the expression below by taking out its greatest common factor? $\newline$ $10x^{2}+50x=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $10x(x^{2}+5x)$ $\newline$ (B) $x(10x^{2}+50x)$ $\newline$ (C) $10x(x+5)$ $\newline$ (D) $x(10x+50)$

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Factor quadratics

Full solution

Q. Which expression is the result of factoring the expression below by taking out its greatest common factor?

\newline

10x^{2}+50x=?

\newline

Choose

1

answer:

\newline

(A)

10x(x^{2}+5x)

\newline

(B)

x(10x^{2}+50x)

\newline

(C)

10x(x+5)

\newline

(D)

x(10x+50)

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the expression $10x^2 + 50x$ . $\newline$ The GCF of $10x^2$ and $50x$ is $10x$ , because $10x$ is the largest expression that divides both terms evenly.
Factor out GCF from each term: Factor out the GCF from each term in the expression. $\newline$ Divide each term by the GCF $10x$ and write the expression as the product of the GCF and the resulting terms. $\newline$ $10x^2 \div 10x = x$ $\newline$ $50x \div 10x = 5$ $\newline$ The factored expression is $10x(x + 5)$ .
Write expression as product: Match the factored expression with the correct answer choice. $\newline$ The factored expression $10x(x + 5)$ corresponds to answer choice (C).

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