Factor. z^2 + 12z + 11 ____

Identify Coefficients: Identify the coefficients for z^2, z, and the constant term. The quadratic expression is in the form z^2 + bz + c, where b is the coefficient of z, and c is the constant term. For z^2 + 12z + 11, b = 12 and c = 11.Find Multiplying Numbers: Find two numbers that multiply to c (11) and add up to b (12). We need to find two numbers m and n such that m * n = 11 and m + n = 12. The numbers 1 and 11 satisfy these conditions because 1 * 11 = 11 and 1 + 11 = 12.Write Factored Form: Write the factored form using the numbers found in the previous step. The factored form of the quadratic expression is (z + m)(z + n). Substitute m = 1 and n = 11 into the factored form to get (z + 1)(z + 11).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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z^2 + 12z + 11

Identify Coefficients: Identify the coefficients for $z^2$ , $z$ , and the constant term. $\newline$ The quadratic expression is in the form $z^2 + bz + c$ , where $b$ is the coefficient of $z$ , and $c$ is the constant term. $\newline$ For $z^2 + 12z + 11$ , $b = 12$ and $c = 11$ .
Find Multiplying Numbers: Find two numbers that multiply to $c (11)$ and add up to $b (12)$ . We need to find two numbers $m$ and $n$ such that $m \times n = 11$ and $m + n = 12$ . The numbers $1$ and $11$ satisfy these conditions because $1 \times 11 = 11$ and $1 + 11 = 12$ .
Write Factored Form: Write the factored form using the numbers found in the previous step. $\newline$ The factored form of the quadratic expression is $(z + m)(z + n)$ . $\newline$ Substitute $m = 1$ and $n = 11$ into the factored form to get $(z + 1)(z + 11)$ .