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Factor. $\newline$ $t^2 + 14t + 13$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

t^2 + 14t + 13

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $t^2 + 14t + 13$ . Compare $t^2 + 14t + 13$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 14$ , and $c = 13$ .
Find Product and Sum: Find two numbers whose product is equal to $a*c$ (which is $13$ ) and whose sum is equal to $b$ (which is $14$ ). $\newline$ We need to find two numbers that multiply to $13$ and add up to $14$ . $\newline$ The numbers $1$ and $13$ satisfy these conditions because: $\newline$ $1 \times 13 = 13$ (product) $\newline$ $1 + 13 = 14$ (sum)
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(t + 1)(t + 13)$ .

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