Factor. z^2 + 8z + 15 ____

Identify Variables: Identify a, b, and c in the quadratic expression z^2 + 8z + 15. The quadratic expression is in the standard form z^2 + bz + c, where a = 1, b = 8, and c = 15.Find Multiplying Numbers: Find two numbers that multiply to c (15) and add up to b (8). We need to find two numbers that multiply together to give 15 and when added together give 8. The numbers 3 and 5 satisfy these conditions because 3 * 5 = 15 and 3 + 5 = 8.Write Factored Form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (z + 3)(z + 5), because these two binomials multiply out to the original quadratic expression z^2 + 8z + 15.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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z^2 + 8z + 15

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $z^2 + 8z + 15$ . The quadratic expression is in the standard form $z^2 + bz + c$ , where $a = 1$ , $b = 8$ , and $c = 15$ .
Find Multiplying Numbers: Find two numbers that multiply to $c$ ( $15$ ) and add up to $b$ ( $8$ ). $\newline$ We need to find two numbers that multiply together to give $15$ and when added together give $8$ . The numbers $3$ and $5$ satisfy these conditions because $3 \times 5 = 15$ and $3 + 5 = 8$ .
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(z + 3)(z + 5)$ , because these two binomials multiply out to the original quadratic expression $z^2 + 8z + 15$ .