Factor completely. 2t^(2)+7t+6

Identify a, b, c: Identify a, b, and c in the quadratic expression 2t^2+7t+6. Compare 2t^2+7t+6 with ax^2+bx+c. a = 2 b = 7 c = 6Find two numbers: Find two numbers that multiply to a*c (which is 2*6=12) and add up to b (which is 7). The two numbers that satisfy these conditions are 3 and 4, since 3*4=12 and 3+4=7.Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step 2. 2t^2+7t+6 can be rewritten as 2t^2+3t+4t+6 by splitting the middle term into 3t and 4t.Factor by grouping: Factor by grouping. Group the terms into two pairs: (2t^2+3t) and (4t+6). Factor out the greatest common factor from each pair. From the first pair, factor out t: t(2t+3). From the second pair, factor out 2: 2(2t+3).Write factored form: Write the factored form of the expression. Since both groups contain the common factor (2t+3), factor this out. The factored form is (t+2)(2t+3).

Home

Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor completely.

\newline

2t^{2}+7t+6

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2t^2+7t+6$ . Compare $2t^2+7t+6$ with $ax^2+bx+c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $2*6=12$ ) and add up to $b$ (which is $7$ ). $\newline$ The two numbers that satisfy these conditions are $3$ and $4$ , since $3*4=12$ and $3+4=7$ .
Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step $2$ . $\newline$ $2t^2+7t+6$ can be rewritten as $2t^2+3t+4t+6$ by splitting the middle term into $3t$ and $4t$ .
Factor by grouping: Factor by grouping. Group the terms into two pairs: $2t^2+3t$ and $4t+6$ . Factor out the greatest common factor from each pair. From the first pair, factor out $t$ : $t(2t+3)$ . From the second pair, factor out $2$ : $2(2t+3)$ .
Write factored form: Write the factored form of the expression. $\newline$ Since both groups contain the common factor $(2t+3)$ , factor this out. $\newline$ The factored form is $(t+2)(2t+3)$ .