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

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 3w^2 + 11w + 6 by comparing it to the standard form ax^2 + bx + c. a = 3 b = 11 c = 6Find two numbers: Find two numbers that multiply to a*c (3*6 = 18) and add up to b (11). The two numbers that satisfy these conditions are 2 and 9 because 2*9 = 18 and 2+9 = 11.Rewrite middle term: Rewrite the middle term 11w using the two numbers found in the previous step. 3w^2 + 11w + 6 can be rewritten as 3w^2 + 2w + 9w + 6.Group and factor: Group the terms into two pairs and factor by grouping. Group (3w^2 + 2w) and (9w + 6). Factor out the greatest common factor from each group. From (3w^2 + 2w), factor out w: w(3w + 2). From (9w + 6), factor out 3: 3(3w + 2).Notice common factor: Notice that both groups now contain the common factor (3w + 2). Write the expression as the product of this common factor and the other factors. The factored form is (w + 3)(3w + 2).

Home

Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

\newline

3w^2 + 11w + 6

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $3w^2 + 11w + 6$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 3$ $b = 11$ $c = 6$
Find two numbers: Find two numbers that multiply to $a*c$ ( $3*6 = 18$ ) and add up to $b$ ( $11$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $9$ because $2*9 = 18$ and $2+9 = 11$ .
Rewrite middle term: Rewrite the middle term $11w$ using the two numbers found in the previous step. $\newline$ $3w^2 + 11w + 6$ can be rewritten as $3w^2 + 2w + 9w + 6$ .
Group and factor: Group the terms into two pairs and factor by grouping. $\newline$ Group $(3w^2 + 2w)$ and $(9w + 6)$ . $\newline$ Factor out the greatest common factor from each group. $\newline$ From $(3w^2 + 2w)$ , factor out $w$ : $w(3w + 2)$ . $\newline$ From $(9w + 6)$ , factor out $3$ : $3(3w + 2)$ .
Notice common factor: Notice that both groups now contain the common factor $3w + 2$ . Write the expression as the product of this common factor and the other factors. The factored form is $w + 3)(3w + 2$ .