Factor. p^2 + 13p + 22 ____

Identify b and c: Identify b and c in the quadratic expression p^2 + 13p + 22. Compare p^2 + 13p + 22 with the standard quadratic form x^2 + bx + c. Here, b = 13 and c = 22.Compare with standard form: Find two numbers whose product is c (22) and whose sum is b (13). We need to find two numbers that multiply to 22 and add up to 13. The numbers 2 and 11 satisfy these conditions because: 2 * 11 = 22 (product condition) 2 + 11 = 13 (sum condition)Find product and sum: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (p + 2)(p + 11).

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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 + 13p + 22

Identify $b$ and $c$ : Identify $b$ and $c$ in the quadratic expression $p^2 + 13p + 22$ . Compare $p^2 + 13p + 22$ with the standard quadratic form $x^2 + bx + c$ . Here, $b = 13$ and $c = 22$ .
Compare with standard form: Find two numbers whose product is $c (22)$ and whose sum is $b (13)$ . We need to find two numbers that multiply to $22$ and add up to $13$ . The numbers $2$ and $11$ satisfy these conditions because: $2 \times 11 = 22$ (product condition) $2 + 11 = 13$ (sum condition)
Find product and sum: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(p + 2)(p + 11)$ .