Factor the trinomial: 5x^(2)+12 x+4 Answer:

Identify a, b, c: Identify a, b, and c in the trinomial 5x^2 + 12x + 4. Compare 5x^2 + 12x + 4 with ax^2 + bx + c. a = 5 b = 12 c = 4Find two numbers: Find two numbers whose product is a*c (5*4 = 20) and whose sum is b (12). We need to find two numbers that multiply to 20 and add up to 12. The numbers 2 and 10 satisfy these conditions because: 2 * 10 = 20 2 + 10 = 12Rewrite middle term: Rewrite the middle term (12x) using the two numbers found in Step 2. 5x^2 + 2x + 10x + 4 Now we have four terms instead of three, which we can factor by grouping.Group and factor: Group the terms and factor each group. (5x^2 + 2x) + (10x + 4) Factor out the greatest common factor from each group. x(5x + 2) + 2(5x + 2)Factor common binomial: Factor out the common binomial factor. The common binomial factor is (5x + 2). So, the factored form of the trinomial is: (x + 2)(5x + 2)

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Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor the trinomial:

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5 x^{2}+12 x+4

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the trinomial $5x^2 + 12x + 4$ . Compare $5x^2 + 12x + 4$ with $ax^2 + bx + c$ . $a = 5$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $5*4 = 20$ ) and whose sum is $b$ ( $12$ ). $\newline$ We need to find two numbers that multiply to $20$ and add up to $12$ . $\newline$ The numbers $2$ and $10$ satisfy these conditions because: $\newline$ $2 * 10 = 20$ $\newline$ $2 + 10 = 12$
Rewrite middle term: Rewrite the middle term $12x$ using the two numbers found in Step $2$ . $5x^2 + 2x + 10x + 4$ Now we have four terms instead of three, which we can factor by grouping.
Group and factor: Group the terms and factor each group. $\newline$ $(5x^2 + 2x) + (10x + 4)$ $\newline$ Factor out the greatest common factor from each group. $\newline$ $x(5x + 2) + 2(5x + 2)$
Factor common binomial: Factor out the common binomial factor. $\newline$ The common binomial factor is $(5x + 2)$ . $\newline$ So, the factored form of the trinomial is: $\newline$ $(x + 2)(5x + 2)$