Factor. q^2 + 8q + 12 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression q^2 + 8q + 12. The quadratic expression is in the standard form aq^2 + bq + c, where a = 1, b = 8, and c = 12.Find Multiplying Numbers: Find two numbers that multiply to c (12) and add up to b (8). We need to find two numbers that multiply together to give 12 and when added together give 8. The numbers 2 and 6 satisfy these conditions because 2 * 6 = 12 and 2 + 6 = 8.Write Factored Form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (q + 2)(q + 6), because when we apply the distributive property (FOIL), we get back the original expression: q^2 + 2q + 6q + 12, which simplifies to q^2 + 8q + 12.

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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 + 8q + 12

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $q^2 + 8q + 12$ . $\newline$ The quadratic expression is in the standard form $aq^2 + bq + c$ , where $a = 1$ , $b = 8$ , and $b$ $0$ .
Find Multiplying Numbers: Find two numbers that multiply to $c$ ( $12$ ) and add up to $b$ ( $8$ ). $\newline$ We need to find two numbers that multiply together to give $12$ and when added together give $8$ . The numbers $2$ and $6$ satisfy these conditions because $2 \times 6 = 12$ and $2 + 6 = 8$ .
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(q + 2)(q + 6)$ , because when we apply the distributive property (FOIL), we get back the original expression: $q^2 + 2q + 6q + 12$ , which simplifies to $q^2 + 8q + 12$ .