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Factor. $\newline$ $4w^2 + 8w + 3$

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Factor quadratics with other leading coefficients

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Q. Factor.

\newline

4w^2 + 8w + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $4w^2 + 8w + 3$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 4$ $\newline$ $b = 8$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $4*3=12$ ) and add up to $b$ (which is $8$ ). $\newline$ After trying different combinations, we find that the numbers $2$ and $6$ work because: $\newline$ $2 \times 6 = 12$ $\newline$ $2 + 6 = 8$
Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in the previous step. $\newline$ $4w^2 + 8w + 3$ can be rewritten as $4w^2 + 2w + 6w + 3$ .
Group terms and factor: Group the terms in pairs and factor out the common factors from each pair. $\newline$ From the first pair $4w^2 + 2w$ , factor out $2w$ : $\newline$ $2w(2w + 1)$ $\newline$ From the second pair $6w + 3$ , factor out $3$ : $\newline$ $3(2w + 1)$
Factor out common binomial: Notice that both groups have a common binomial factor $2w + 1$ . Factor out the common binomial factor to write the expression in factored form. $\newline$ The factored form is $2w + 1$ $2w + 3$ .

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