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Factor. $\newline$ $h^2 + 5h + 4$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

h^2 + 5h + 4

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $h^2 + 5h + 4$ . Compare $h^2 + 5h + 4$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find Multiplying Numbers: Find two numbers that multiply to $a*c$ (which is $4$ , since $a = 1$ ) and add up to $b$ (which is $5$ ). $\newline$ The two numbers that satisfy these conditions are $4$ and $1$ because: $\newline$ $4 \times 1 = 4$ $\newline$ $4 + 1 = 5$
Write Split Middle Term: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ $h^2 + 4h + 1h + 4$
Factor by Grouping: Factor by grouping. Group the terms to create two binomials. $\newline$ $(h^2 + 4h) + (1h + 4)$
Factor Common Factors: Factor out the common factors from each group. $\newline$ $h(h + 4) + 1(h + 4)$
Factor Common Binomial: Factor out the common binomial factor $(h + 4)$ . $\newline$ $(h + 1)(h + 4)$

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