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Factor. $\newline$ $5h^2 - 20h + 15$

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Factor polynomials

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Q. Factor.

\newline

5h^2 - 20h + 15

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5h^2 - 20h + 15$ . $\newline$ $a = 5$ $\newline$ $b = -20$ $\newline$ $c = 15$
Find Multiplying Numbers: Look for two numbers that multiply to $a*c$ ( $5*15 = 75$ ) and add up to $b$ ( $-20$ ). $\newline$ Hmm, let's see... $-5$ and $-15$ work. $\newline$ $-5 * -15 = 75$ $\newline$ $-5 + -15 = -20$
Split Middle Term: Write the quadratic expression by splitting the middle term using the two numbers found. $\newline$ $5h^2 - 5h - 15h + 15$
Factor by Grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms. $\newline$ $(5h^2 - 5h) - (15h - 15)$
Factor Common Factors: Factor out the common factors in each group. $\newline$ $5h(h - 1) - 15(h - 1)$
Factor Common Binomial: Factor out the common binomial factor $(h - 1)$ . $\newline$ $(5h - 15)(h - 1)$
Factor Common Factor: Factor out the common factor of $5$ from the first binomial. $\newline$ $5(h - 3)(h - 1)$

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