Factor. f^2 + 14f + 13 ____

Identify Coefficients: Identify the coefficients for f^2, f, and the constant term in the quadratic expression f^2 + 14f + 13. The coefficient of f^2 is 1 (a = 1), the coefficient of f is 14 (b = 14), and the constant term is 13 (c = 13).Find Two Numbers: We need to find two numbers that multiply to give the constant term, 13, and add up to give the coefficient of the f term, 14. The numbers that satisfy these conditions are 1 and 13 because 1 * 13 = 13 and 1 + 13 = 14.Write Factored Form: Write the factored form of the quadratic expression using the two numbers found in the previous step. The factored form is (f + 1)(f + 13).Check Factored Form: Check the factored form by expanding (f + 1)(f + 13) to ensure it equals the original expression f^2 + 14f + 13. Expanding the factored form gives f^2 + 13f + f + 13, which simplifies to f^2 + 14f + 13.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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f^2 + 14f + 13

Identify Coefficients: Identify the coefficients for $f^2$ , $f$ , and the constant term in the quadratic expression $f^2 + 14f + 13$ . The coefficient of $f^2$ is $1$ ( $a = 1$ ), the coefficient of $f$ is $14$ ( $b = 14$ ), and the constant term is $13$ ( $f$ $0$ ).
Find Two Numbers: We need to find two numbers that multiply to give the constant term, $13$ , and add up to give the coefficient of the $f$ term, $14$ . The numbers that satisfy these conditions are $1$ and $13$ because $1 \times 13 = 13$ and $1 + 13 = 14$ .
Write Factored Form: Write the factored form of the quadratic expression using the two numbers found in the previous step. $\newline$ The factored form is $(f + 1)(f + 13)$ .
Check Factored Form: Check the factored form by expanding $(f + 1)(f + 13)$ to ensure it equals the original expression $f^2 + 14f + 13$ . Expanding the factored form gives $f^2 + 13f + f + 13$ , which simplifies to $f^2 + 14f + 13$ .