Factor. 2t^2 + 9t + 10 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 2t^2 + 9t + 10. Compare 2t^2 + 9t + 10 with ax^2 + bx + c. a = 2 b = 9 c = 10Find two numbers: Find two numbers that multiply to a*c (which is 2*10 = 20) and add up to b (which is 9). The two numbers that satisfy these conditions are 5 and 4, since 5*4 = 20 and 5+4 = 9.Rewrite middle term: Rewrite the middle term, 9t, using the two numbers found in Step 2. 2t^2 + 9t + 10 can be expressed as 2t^2 + 5t + 4t + 10.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms: (2t^2 + 5t) + (4t + 10) Factor out the greatest common factor from each group: t(2t + 5) + 2(2t + 5)Factor out common binomial: Factor out the common binomial factor. Since both groups contain the common factor (2t + 5), factor it out: (t + 2)(2t + 5)

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2t^2 + 9t + 10

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2t^2 + 9t + 10$ . Compare $2t^2 + 9t + 10$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $2*10 = 20$ ) and add up to $b$ (which is $9$ ). $\newline$ The two numbers that satisfy these conditions are $5$ and $4$ , since $5*4 = 20$ and $5+4 = 9$ .
Rewrite middle term: Rewrite the middle term, $9t$ , using the two numbers found in Step $2$ . $\newline$ $2t^2 + 9t + 10$ can be expressed as $2t^2 + 5t + 4t + 10$ .
Factor by grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms: $\newline$ $(2t^2 + 5t) + (4t + 10)$ $\newline$ Factor out the greatest common factor from each group: $\newline$ $t(2t + 5) + 2(2t + 5)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ Since both groups contain the common factor $(2t + 5)$ , factor it out: $\newline$ $(t + 2)(2t + 5)$