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Factor. $\newline$ $x^2 + 20x + 19$

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Factor quadratics with leading coefficient 1

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Q. Factor.

\newline

x^2 + 20x + 19

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $x^2 + 20x + 19$ . $\newline$ The quadratic expression is in the form $ax^2 + bx + c$ , where $a = 1$ , $b = 20$ , and $b$ $0$ .
Find Factors and Sum: Find two numbers that multiply to $c$ ( $19$ ) and add up to $b$ ( $20$ ). $\newline$ We need to find two numbers $m$ and $n$ such that $m \times n = 19$ and $m + n = 20$ . $\newline$ Since $19$ is a prime number, the only factors of $19$ are $19$ $0$ and $19$ itself. $\newline$ $19$ $2$ and $19$ $3$ , so the numbers are $19$ $0$ and $19$ .
Write Factored Form: Write the factored form using the numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(x + m)(x + n)$ , where $m = 1$ and $n = 19$ . $\newline$ Therefore, the factored form is $(x + 1)(x + 19)$ .

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