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$3n^2+5n+2$

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Factor quadratics with other leading coefficients

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Q.

3n^2+5n+2

Identify variables: Identify $a$ , $b$ , and $c$ by comparing $3n^2+5n+2$ with $ax^2+bx+c$ . $\newline$ $a = 3$ , $b = 5$ , $c = 2$ .
Find multiplication numbers: Find two numbers that multiply to $a*c$ ( $3*2=6$ ) and add up to $b$ ( $5$ ). $\newline$ The numbers are $2$ and $3$ because $2*3=6$ and $2+3=5$ .
Rewrite middle term: Rewrite the middle term using the two numbers found. $3n^2+5n+2$ becomes $3n^2+2n+3n+2$ .
Factor by grouping: Factor by grouping. $\newline$ Take out the common factor of $n$ from the first two terms: $n(3n+2)$ . $\newline$ Take out the common factor of $1$ from the last two terms: $1(3n+2)$ .
Write factored form: Write the factored form by taking out the common binomial. The factored form is $(n+1)(3n+2)$ .

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