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

Identify a, b, c: Identify a, b, and c in the quadratic expression 3q^2 + 5q + 2. Compare 3q^2 + 5q + 2 with ax^2 + bx + c. a = 3 b = 5 c = 2Find two numbers: Find two numbers that multiply to a*c (which is 3*2=6) and add up to b (which is 5). The two numbers that satisfy these conditions are 2 and 3 because: 2 * 3 = 6 2 + 3 = 5Rewrite middle term: Rewrite the middle term (5q) using the two numbers found in Step 2. 3q^2 + 5q + 2 can be rewritten as 3q^2 + 2q + 3q + 2.Factor by grouping: Factor by grouping. Group the terms into two pairs: (3q^2 + 2q) and (3q + 2). Factor out the greatest common factor from each pair. From the first pair, factor out q: q(3q + 2). From the second pair, factor out 1: 1(3q + 2).Write factored form: Write the factored form of the expression. Since both groups contain the factor (3q + 2), factor this out: q(3q + 2) + 1(3q + 2) = (q + 1)(3q + 2).

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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3q^2 + 5q + 2

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3q^2 + 5q + 2$ . Compare $3q^2 + 5q + 2$ with $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $3*2=6$ ) and add up to $b$ (which is $5$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $3$ because: $\newline$ $2 * 3 = 6$ $\newline$ $2 + 3 = 5$
Rewrite middle term: Rewrite the middle term $5q$ using the two numbers found in Step $2$ . $3q^2 + 5q + 2$ can be rewritten as $3q^2 + 2q + 3q + 2$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $3q^2 + 2q$ and $3q + 2$ . $\newline$ Factor out the greatest common factor from each pair. $\newline$ From the first pair, factor out $q$ : $q(3q + 2)$ . $\newline$ From the second pair, factor out $1$ : $1(3q + 2)$ .
Write factored form: Write the factored form of the expression. $\newline$ Since both groups contain the factor $(3q + 2)$ , factor this out: $\newline$ $q(3q + 2) + 1(3q + 2) = (q + 1)(3q + 2)$ .