Factor. p^2 + 5p + 6 ____

Identify Variables: Identify a, b, and c in the quadratic expression p^2 + 5p + 6. The quadratic expression is in the form p^2 + bp + c, where a = 1, b = 5, and c = 6.Find Two Numbers: Find two numbers that multiply to c (6) and add up to b (5). We need to find two numbers that when multiplied give 6 and when added give 5. The numbers 2 and 3 satisfy these conditions because 2 * 3 = 6 and 2 + 3 = 5.Write Factored Form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (p + 2)(p + 3), because these two binomials multiply to give the original quadratic expression.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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p^2 + 5p + 6

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $p^2 + 5p + 6$ . The quadratic expression is in the form $p^2 + bp + c$ , where $a = 1$ , $b = 5$ , and $c = 6$ .
Find Two Numbers: Find two numbers that multiply to $c (6)$ and add up to $b (5)$ . We need to find two numbers that when multiplied give $6$ and when added give $5$ . The numbers $2$ and $3$ satisfy these conditions because $2 \times 3 = 6$ and $2 + 3 = 5$ .
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(p + 2)(p + 3)$ , because these two binomials multiply to give the original quadratic expression.