Factor. 3q^2 + 8q + 5 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 3q^2 + 8q + 5. Compare 3q^2 + 8q + 5 with the standard form ax^2 + bx + c. a = 3 b = 8 c = 5Find Factors and Sum: Find two numbers that multiply to a*c (which is 3*5=15) and add up to b (which is 8). We need to find two numbers that satisfy these conditions. After checking possible pairs of factors of 15, we find that 3 and 5 are the numbers we are looking for because 3*5 = 15 and 3+5 = 8.Rewrite Middle Term: Rewrite the middle term 8q using the two numbers found in Step 2. 3q^2 + 8q + 5 can be rewritten as 3q^2 + 3q + 5q + 5.Factor by Grouping: Factor by grouping. Group the first two terms and the last two terms separately. (3q^2 + 3q) + (5q + 5) Factor out the greatest common factor from each group. 3q(q + 1) + 5(q + 1)Factor out Common Binomial: Factor out the common binomial factor (q + 1). 3q(q + 1) + 5(q + 1) can be factored as (q + 1)(3q + 5).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3q^2 + 8q + 5

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3q^2 + 8q + 5$ . Compare $3q^2 + 8q + 5$ with the standard form $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find Factors and Sum: Find two numbers that multiply to $a*c$ (which is $3*5=15$ ) and add up to $b$ (which is $8$ ). $\newline$ We need to find two numbers that satisfy these conditions. $\newline$ After checking possible pairs of factors of $15$ , we find that $3$ and $5$ are the numbers we are looking for because $3*5 = 15$ and $3+5 = 8$ .
Rewrite Middle Term: Rewrite the middle term $8q$ using the two numbers found in Step $2$ . $3q^2 + 8q + 5$ can be rewritten as $3q^2 + 3q + 5q + 5$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms separately. $\newline$ $(3q^2 + 3q) + (5q + 5)$ $\newline$ Factor out the greatest common factor from each group. $\newline$ $3q(q + 1) + 5(q + 1)$
Factor out Common Binomial: Factor out the common binomial factor $(q + 1)$ . $3q(q + 1) + 5(q + 1)$ can be factored as $(q + 1)(3q + 5)$ .