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Factor. $\newline$ $p^2 + 6p + 8$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

p^2 + 6p + 8

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $p^2 + 6p + 8$ . $\newline$ The quadratic expression is in the form $ap^2 + bp + c$ , where $a = 1$ , $b = 6$ , and $b$ $0$ .
Find two numbers: Find two numbers that multiply to $c$ (which is $8$ ) and add up to $b$ (which is $6$ ). $\newline$ We need to find two numbers that multiply to $8$ and add up to $6$ . The numbers $2$ and $4$ satisfy these conditions because: $\newline$ $2 \times 4 = 8$ (product is $c$ ) $\newline$ $8$ $0$ (sum is $b$ )
Write factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(p + 2)(p + 4)$ , because: $\newline$ $(p + 2)(p + 4) = p^2 + 4p + 2p + 8 = p^2 + 6p + 8$

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