Factor. 7f^2 + 10f + 3 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 7f^2 + 10f + 3. Compare 7f^2 + 10f + 3 with the standard form ax^2 + bx + c. a = 7 b = 10 c = 3Find numbers multiply add: Find two numbers that multiply to a*c (7*3=21) and add up to b (10). We need to find two numbers that multiply to 21 and add up to 10. After checking possible pairs of factors of 21 (1 and 21, 3 and 7), we find that 1 and 21 do not add up to 10, but 3 and 7 do. So, the two numbers are 3 and 7.Rewrite middle term: Rewrite the middle term 10f using the two numbers found in Step 2. We can express 10f as 3f + 7f. So, 7f^2 + 10f + 3 becomes 7f^2 + 3f + 7f + 3.Factor by grouping: Factor by grouping. Now we group the terms: (7f^2 + 3f) + (7f + 3). Factor out the greatest common factor from each group. From 7f^2 + 3f, we can factor out f, giving us f(7f + 3). From 7f + 3, we can factor out 1, giving us 1(7f + 3).Factor common binomial: Factor out the common binomial factor. We now have f(7f + 3) + 1(7f + 3). The common binomial factor is (7f + 3). Factoring out (7f + 3) gives us (7f + 3)(f + 1).

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Factor. $\newline$ $7f^2 + 10f + 3$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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7f^2 + 10f + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $7f^2 + 10f + 3$ . Compare $7f^2 + 10f + 3$ with the standard form $ax^2 + bx + c$ . $a = 7$ $b$ $0$ $b$ $1$
Find numbers multiply add: Find two numbers that multiply to $a*c$ ( $7*3=21$ ) and add up to $b$ ( $10$ ). $\newline$ We need to find two numbers that multiply to $21$ and add up to $10$ . $\newline$ After checking possible pairs of factors of $21$ ( $1$ and $21$ , $3$ and $7*3=21$ $0$ ), we find that $1$ and $21$ do not add up to $10$ , but $3$ and $7*3=21$ $0$ do. $\newline$ So, the two numbers are $3$ and $7*3=21$ $0$ .
Rewrite middle term: Rewrite the middle term $10f$ using the two numbers found in Step $2$ . $\newline$ We can express $10f$ as $3f + 7f$ . $\newline$ So, $7f^2 + 10f + 3$ becomes $7f^2 + 3f + 7f + 3$ .
Factor by grouping: Factor by grouping. $\newline$ Now we group the terms: $7f^2 + 3f$ + $7f + 3$ . $\newline$ Factor out the greatest common factor from each group. $\newline$ From $7f^2 + 3f$ , we can factor out $f$ , giving us $f(7f + 3)$ . $\newline$ From $7f + 3$ , we can factor out $1$ , giving us $1(7f + 3)$ .
Factor common binomial: Factor out the common binomial factor. $\newline$ We now have $f(7f + 3) + 1(7f + 3)$ . $\newline$ The common binomial factor is $(7f + 3)$ . $\newline$ Factoring out $(7f + 3)$ gives us $(7f + 3)(f + 1)$ .