Factor. z^2 + 13z + 22 ______

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is z^2 + 13z + 22. Here, the coefficient of z^2 (a) is 1, the coefficient of z (b) is 13, and the constant term (c) is 22.Find Two Numbers: Find two numbers that multiply to give the constant term (c) and add up to the coefficient of z (b). We need to find two numbers whose product is 22 (the constant term) and whose sum is 13 (the coefficient of z). The numbers 2 and 11 satisfy these conditions because 2 * 11 = 22 and 2 + 11 = 13.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression z^2 + 13z + 22 is (z + 2)(z + 11), since these factors will multiply out to the original quadratic expression.

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Factor. $\newline$ $z^2 + 13z + 22$ $\newline$ ______

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Q. Factor.

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z^2 + 13z + 22

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Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $z^2 + 13z + 22$ . Here, the coefficient of $z^2$ $(a)$ is $1$ , the coefficient of $z$ $(b)$ is $13$ , and the constant term $(c)$ is $22$ .
Find Two Numbers: Find two numbers that multiply to give the constant term $c$ and add up to the coefficient of $z$ ( $b$ ). $\newline$ We need to find two numbers whose product is $22$ (the constant term) and whose sum is $13$ (the coefficient of $z$ ). The numbers $2$ and $11$ satisfy these conditions because $2 \times 11 = 22$ and $2 + 11 = 13$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression $z^2 + 13z + 22$ is $(z + 2)(z + 11)$ , since these factors will multiply out to the original quadratic expression.