Factor. f^2 + 10f + 16 ____

Identify Coefficients: Identify the coefficients for f^2, f, and the constant term in the quadratic expression f^2 + 10f + 16. Comparing f^2 + 10f + 16 with the standard quadratic form af^2 + bf + c, we find that a = 1 (coefficient of f^2), b = 10 (coefficient of f), and c = 16 (constant term).Find Multiplying Numbers: Determine two numbers that multiply to give c (16) and add up to give b (10). We are looking for two numbers that when multiplied give 16 and when added give 10. The pair of numbers that satisfy these conditions are 2 and 8 because 2 * 8 = 16 and 2 + 8 = 10.Write Factored Form: Write the factored form of the quadratic expression using the two numbers found in the previous step. The factored form of the quadratic expression is (f + 2)(f + 8) because these two binomials multiply to give the original quadratic expression f^2 + 10f + 16.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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f^2 + 10f + 16

Identify Coefficients: Identify the coefficients for $f^2$ , $f$ , and the constant term in the quadratic expression $f^2 + 10f + 16$ . Comparing $f^2 + 10f + 16$ with the standard quadratic form $af^2 + bf + c$ , we find that $a = 1$ (coefficient of $f^2$ ), $b = 10$ (coefficient of $f$ ), and $c = 16$ (constant term).
Find Multiplying Numbers: Determine two numbers that multiply to give $c (16)$ and add up to give $b (10)$ . We are looking for two numbers that when multiplied give $16$ and when added give $10$ . The pair of numbers that satisfy these conditions are $2$ and $8$ because $2 \times 8 = 16$ and $2 + 8 = 10$ .
Write Factored Form: Write the factored form of the quadratic expression using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression is $(f + 2)(f + 8)$ because these two binomials multiply to give the original quadratic expression $f^2 + 10f + 16$ .