Factor. 5t^2 + 12t + 4 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 5t^2 + 12t + 4 by comparing it with the standard form ax^2 + bx + c. a = 5 b = 12 c = 4Find two numbers: Find two numbers that multiply to a*c (which is 5*4=20) and add up to b (which is 12). The two numbers that satisfy these conditions are 10 and 2 because 10*2=20 and 10+2=12.Rewrite middle term: Rewrite the middle term, 12t, using the two numbers found in the previous step. 5t^2 + 12t + 4 can be rewritten as 5t^2 + 10t + 2t + 4.Group terms for factoring: Group the terms into two pairs to factor by grouping. (5t^2 + 10t) + (2t + 4)Factor out common factor: Factor out the greatest common factor from each pair. 5t(t + 2) + 2(t + 2)Factor out (t + 2): Since (t + 2) is a common factor in both groups, factor it out. (5t + 2)(t + 2) is the factored form of the quadratic expression.

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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5t^2 + 12t + 4

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5t^2 + 12t + 4$ by comparing it with the standard form $ax^2 + bx + c$ .
$a = 5$
$b = 12$
$b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $5*4=20$ ) and add up to $b$ (which is $12$ ). $\newline$ The two numbers that satisfy these conditions are $10$ and $2$ because $10*2=20$ and $10+2=12$ .
Rewrite middle term: Rewrite the middle term, $12t$ , using the two numbers found in the previous step. $\newline$ $5t^2 + 12t + 4$ can be rewritten as $5t^2 + 10t + 2t + 4$ .
Group terms for factoring: Group the terms into two pairs to factor by grouping. $\newline$ $(5t^2 + 10t) + (2t + 4)$
Factor out common factor: Factor out the greatest common factor from each pair. $5t(t + 2) + 2(t + 2)$
Factor out $(t + 2)$ : Since $(t + 2)$ is a common factor in both groups, factor it out. $(5t + 10)(t + 2)$ is the factored form of the quadratic expression.