Factor. 3q^2 + 7q + 4 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 3q^2 + 7q + 4. Compare 3q^2 + 7q + 4 with the standard form ax^2 + bx + c. a = 3 b = 7 c = 4Find factors and sum: Find two numbers that multiply to a*c (which is 3*4=12) and add up to b (which is 7). We need to find two numbers that satisfy these conditions. After checking possible pairs of factors of 12, we find that 3 and 4 are the numbers we are looking for because 3*4 = 12 and 3 + 4 = 7.Rewrite middle term: Rewrite the middle term 7q using the two numbers 3 and 4 found in Step 2. 3q^2 + 7q + 4 can be rewritten as 3q^2 + 3q + 4q + 4.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms: (3q^2 + 3q) + (4q + 4) Factor out the greatest common factor from each group: 3q(q + 1) + 4(q + 1)Factor out common binomial: Factor out the common binomial factor (q + 1). The expression now looks like 3q(q + 1) + 4(q + 1). We can factor out (q + 1) to get the final factored form: (q + 1)(3q + 4)

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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3q^2 + 7q + 4

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3q^2 + 7q + 4$ . Compare $3q^2 + 7q + 4$ 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 $3*4=12$ ) and add up to $b$ (which is $7$ ). $\newline$ We need to find two numbers that satisfy these conditions. $\newline$ After checking possible pairs of factors of $12$ , we find that $3$ and $4$ are the numbers we are looking for because $3*4 = 12$ and $3 + 4 = 7$ .
Rewrite middle term: Rewrite the middle term $7q$ using the two numbers $3$ and $4$ found in Step $2$ . $\newline$ $3q^2 + 7q + 4$ can be rewritten as $3q^2 + 3q + 4q + 4$ .
Factor by grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms: $\newline$ $(3q^2 + 3q) + (4q + 4)$ $\newline$ Factor out the greatest common factor from each group: $\newline$ $3q(q + 1) + 4(q + 1)$
Factor out common binomial: Factor out the common binomial factor $(q + 1)$ . The expression now looks like $3q(q + 1) + 4(q + 1)$ . We can factor out $(q + 1)$ to get the final factored form: $(q + 1)(3q + 4)$