Factor. 2t^2 + 9t + 4 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2t^2 + 9t + 4 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 4Find two numbers: Find two numbers that multiply to a*c (2*4 = 8) and add up to b (9). The numbers that satisfy these conditions are 1 and 8 because 1*8 = 8 and 1+8 = 9.Rewrite middle term: Rewrite the middle term (9t) using the two numbers found in the previous step. 2t^2 + 9t + 4 can be rewritten as 2t^2 + 1t + 8t + 4.Group and factor: Group the terms into two pairs and factor by grouping. Group (2t^2 + 1t) and (8t + 4). Factor out the greatest common factor from each group. From the first group, factor out t: t(2t + 1). From the second group, factor out 4: 4(2t + 1).Factor out common factor: Notice that both groups now have a common factor of (2t + 1). Factor out the common factor to get the final factored form. The factored form is (t + 4)(2t + 1).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2t^2 + 9t + 4

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2t^2 + 9t + 4$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 9$ , $c = 4$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*4 = 8$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers that satisfy these conditions are $1$ and $8$ because $1*8 = 8$ and $1+8 = 9$ .
Rewrite middle term: Rewrite the middle term $9t$ using the two numbers found in the previous step. $2t^2 + 9t + 4$ can be rewritten as $2t^2 + 1t + 8t + 4$ .
Group and factor: Group the terms into two pairs and factor by grouping. $\newline$ Group $(2t^2 + 1t)$ and $(8t + 4)$ . $\newline$ Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $t$ : $t(2t + 1)$ . $\newline$ From the second group, factor out $4$ : $4(2t + 1)$ .
Factor out common factor: Notice that both groups now have a common factor of $2t + 1$ . Factor out the common factor to get the final factored form. The factored form is $t + 4)(2t + 1$ .