Factor. q^2 + 15q + 14 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression q^2 + 15q + 14. The quadratic expression is in the standard form aq^2 + bq + c, where a = 1, b = 15, and c = 14.Find two numbers: Find two numbers that multiply to c (14) and add up to b (15). We are looking for two numbers that when multiplied give us 14 and when added give us 15. The numbers 1 and 14 fit this requirement because: 1 * 14 = 14 (product is c) 1 + 14 = 15 (sum is b)Write factored form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (q + 1)(q + 14), because: (q + 1)(q + 14) = q^2 + 14q + q + 14 = q^2 + 15q + 14

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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q^2 + 15q + 14

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $q^2 + 15q + 14$ . $\newline$ The quadratic expression is in the standard form $aq^2 + bq + c$ , where $a = 1$ , $b = 15$ , and $b$ $0$ .
Find two numbers: Find two numbers that multiply to $c$ ( $14$ ) and add up to $b$ ( $15$ ). $\newline$ We are looking for two numbers that when multiplied give us $14$ and when added give us $15$ . The numbers $1$ and $14$ fit this requirement because: $\newline$ $1 \times 14 = 14$ (product is $c$ ) $\newline$ $14$ $0$ (sum is $b$ )
Write factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(q + 1)(q + 14)$ , because: $\newline$ $(q + 1)(q + 14) = q^2 + 14q + q + 14 = q^2 + 15q + 14$