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Factor. $\newline$ $h^2 + 18h + 17$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

h^2 + 18h + 17

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $h^2 + 18h + 17$ . Compare $h^2 + 18h + 17$ 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 $a\cdot c$ (which is $1\cdot 17 = 17$ ) and add up to $b$ (which is $18$ ). $\newline$ We need to find two numbers $m$ and $n$ such that: $\newline$ $m \cdot n = 17$ $\newline$ $m + n = 18$ $\newline$ The numbers that satisfy these conditions are $1$ and $17$ because: $\newline$ $1\cdot 17 = 17$ $0$ $\newline$ $1\cdot 17 = 17$ $1$
Rewrite Quadratic Expression: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ $h^2 + 18h + 17$ can be rewritten as: $\newline$ $h^2 + 1h + 17h + 17$
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to factor out the common factors: $\newline$ $h^2 + 1h$ + $17h + 17$ $\newline$ Factor out $h$ from the first group and $17$ from the second group: $\newline$ $h(h + 1) + 17(h + 1)$
Factor Common Binomial: Factor out the common binomial factor $(h + 1)$ : $(h + 1)(h + 17)$

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