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

Identify a, b, c: Identify a, b, and c in the quadratic expression 5q^2 + 8q + 3 by comparing it with the standard form ax^2 + bx + c. a = 5 b = 8 c = 3Find numbers multiply and add: Find two numbers that multiply to a*c (5*3=15) and add up to b (8). We need to find two numbers that multiply to 15 and add up to 8. The numbers 5 and 3 satisfy these conditions because 5*3 = 15 and 5+3 = 8.Rewrite middle term: Rewrite the middle term 8q using the two numbers found in Step 2. 5q^2 + 8q + 3 can be rewritten as 5q^2 + 5q + 3q + 3 by splitting the middle term into 5q and 3q.Factor by grouping: Factor by grouping. Group the terms into two pairs: (5q^2 + 5q) and (3q + 3). Factor out the greatest common factor from each pair. From the first pair, we can factor out 5q: 5q(q + 1). From the second pair, we can factor out 3: 3(q + 1).Write factored form: Write the factored form of the expression. Since both groups contain the factor (q + 1), we can factor this out. The factored form is (5q + 3)(q + 1).

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Factor. $\newline$ $5q^2 + 8q + 3$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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5q^2 + 8q + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5q^2 + 8q + 3$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 5$ $\newline$ $b = 8$ $\newline$ $b$ $0$
Find numbers multiply and add: Find two numbers that multiply to $a*c$ ( $5*3=15$ ) and add up to $b$ ( $8$ ). $\newline$ We need to find two numbers that multiply to $15$ and add up to $8$ . $\newline$ The numbers $5$ and $3$ satisfy these conditions because $5*3 = 15$ and $5+3 = 8$ .
Rewrite middle term: Rewrite the middle term $8q$ using the two numbers found in Step $2$ . $\newline$ $5q^2 + 8q + 3$ can be rewritten as $5q^2 + 5q + 3q + 3$ by splitting the middle term into $5q$ and $3q$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $5q^2 + 5q$ and $3q + 3$ . $\newline$ Factor out the greatest common factor from each pair. $\newline$ From the first pair, we can factor out $5q$ : $5q(q + 1)$ . $\newline$ From the second pair, we can factor out $3$ : $3(q + 1)$ .
Write factored form: Write the factored form of the expression. $\newline$ Since both groups contain the factor $(q + 1)$ , we can factor this out. $\newline$ The factored form is $(5q + 3)(q + 1)$ .