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

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

u^2 + 14u + 13

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $u^2 + 14u + 13$ . Compare $u^2 + 14u + 13$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 14$ , and $c = 13$ .
Find Two Numbers: Find two numbers that multiply to $c$ ( $13$ ) and add up to $b$ ( $14$ ). $\newline$ We need to find two numbers $m$ and $n$ such that: $\newline$ $m \times n = 13$ $\newline$ $m + n = 14$ $\newline$ Since $13$ is a prime number, the only factors of $13$ are $13$ $0$ and $13$ itself. $\newline$ $13$ $2$ $\newline$ $13$ $3$ $\newline$ So the numbers we are looking for are $13$ $0$ and $13$ .
Write Factored Form: Write the factored form using the numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(u + m)(u + n)$ . $\newline$ Substitute $m = 1$ and $n = 13$ into the factored form. $\newline$ The factored form is $(u + 1)(u + 13)$ .

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