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Factor. $\newline$ $t^2 + 8t + 7$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

t^2 + 8t + 7

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $t^2 + 8t + 7$ . Compare $t^2 + 8t + 7$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 8$ , and $c = 7$ .
Find Two Numbers: Find two numbers that multiply to $c$ ( $7$ ) and add up to $b$ ( $8$ ). $\newline$ We need to find two numbers $m$ and $n$ such that: $\newline$ $m \times n = 7$ (product of $c$ ) $\newline$ $m + n = 8$ (sum of $b$ ) $\newline$ The numbers $7$ $0$ and $7$ satisfy these conditions because: $\newline$ $7$ $2$ $\newline$ $7$ $3$
Write Factored Form: Write the factored form using the numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(t + m)(t + n)$ . $\newline$ Substitute $m = 1$ and $n = 7$ into the factored form to get: $\newline$ $(t + 1)(t + 7)$

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