Factor. 2f^2 + 7f + 5 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2f^2 + 7f + 5 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 7, c = 5Find two numbers: Find two numbers that multiply to a*c (2*5 = 10) and add up to b (7). The numbers that satisfy these conditions are 2 and 5 because 2*5 = 10 and 2+5 = 7.Rewrite middle term: Rewrite the middle term, 7f, using the two numbers found in the previous step: 2f and 5f. The expression becomes 2f^2 + 2f + 5f + 5.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms separately. (2f^2 + 2f) + (5f + 5)Factor out common factor: Factor out the greatest common factor from each group. 2f(f + 1) + 5(f + 1)Final factored form: Since both groups contain the common factor (f + 1), factor it out. The factored form of the expression is (2f + 5)(f + 1).

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2f^2 + 7f + 5

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2f^2 + 7f + 5$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 7$ , $c = 5$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*5 = 10$ ) and add up to $b$ ( $7$ ). $\newline$ The numbers that satisfy these conditions are $2$ and $5$ because $2*5 = 10$ and $2+5 = 7$ .
Rewrite middle term: Rewrite the middle term, $7f$ , using the two numbers found in the previous step: $2f$ and $5f$ . The expression becomes $2f^2 + 2f + 5f + 5$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms separately. $\newline$ $(2f^2 + 2f) + (5f + 5)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $2f(f + 1) + 5(f + 1)$
Final factored form: Since both groups contain the common factor $(f + 1)$ , factor it out. $\newline$ The factored form of the expression is $(2f + 5)(f + 1)$ .