Factor. 6g^2 + 11g + 3 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 6g^2 + 11g + 3. Compare 6g^2 + 11g + 3 with ax^2 + bx + c. a = 6 b = 11 c = 3Find two numbers: Find two numbers that multiply to a*c (6*3=18) and add up to b (11). We need to find two numbers that multiply to 18 and add up to 11. The numbers 2 and 9 satisfy these conditions because 2*9 = 18 and 2+9 = 11.Rewrite middle term: Rewrite the middle term 11g using the two numbers found in Step 2. We can express 11g as the sum of 2g and 9g. 6g^2 + 11g + 3 becomes 6g^2 + 2g + 9g + 3.Factor by grouping: Factor by grouping. Group the terms into two pairs: (6g^2 + 2g) and (9g + 3). Factor out the common factor from each pair. From the first pair, we can factor out 2g: 2g(3g + 1). From the second pair, we can factor out 3: 3(3g + 1).Factor out common binomial: Factor out the common binomial factor. We now have 2g(3g + 1) + 3(3g + 1). The common binomial factor is (3g + 1). Factor this out to get the final factored form: (2g + 3)(3g + 1).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor. $\newline$ $6g^2 + 11g + 3$

View step-by-step help

Home

Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

\newline

6g^2 + 11g + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $6g^2 + 11g + 3$ . Compare $6g^2 + 11g + 3$ with $ax^2 + bx + c$ . $a = 6$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers that multiply to $a*c$ ( $6*3=18$ ) and add up to $b$ ( $11$ ). $\newline$ We need to find two numbers that multiply to $18$ and add up to $11$ . $\newline$ The numbers $2$ and $9$ satisfy these conditions because $2*9 = 18$ and $2+9 = 11$ .
Rewrite middle term: Rewrite the middle term $11g$ using the two numbers found in Step $2$ . $\newline$ We can express $11g$ as the sum of $2g$ and $9g$ . $\newline$ $6g^2 + 11g + 3$ becomes $6g^2 + 2g + 9g + 3$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $6g^2 + 2g$ and $9g + 3$ . $\newline$ Factor out the common factor from each pair. $\newline$ From the first pair, we can factor out $2g$ : $2g(3g + 1)$ . $\newline$ From the second pair, we can factor out $3$ : $3(3g + 1)$ .
Factor out common binomial: Factor out the common binomial factor. $\newline$ We now have $2g(3g + 1) + 3(3g + 1)$ . $\newline$ The common binomial factor is $(3g + 1)$ . $\newline$ Factor this out to get the final factored form: $(2g + 3)(3g + 1)$ .