Factor the trinomial: 2x^(2)+15 x+25 Answer:

Identify a, b, c: Identify a, b, and c in the trinomial 2x^2 + 15x + 25. Compare 2x^2 + 15x + 25 with ax^2 + bx + c. a = 2 b = 15 c = 25Find two numbers: Find two numbers whose product is a*c (2*25 = 50) and whose sum is b (15). We need to find two numbers that multiply to 50 and add up to 15. 10 * 5 = 50 10 + 5 = 15 Two numbers: 10, 5Rewrite middle term: Rewrite the middle term (15x) using the two numbers found in Step 2. 2x^2 + 10x + 5x + 25 Now we have four terms instead of three.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2x^2 + 10x) + (5x + 25) Factor out the greatest common factor from each group. 2x(x + 5) + 5(x + 5)Factor common binomial: Factor out the common binomial factor. The common binomial factor is (x + 5). Factor this out from both groups. (2x + 5)(x + 5)

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Q. Factor the trinomial:

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2 x^{2}+15 x+25

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the trinomial $2x^2 + 15x + 25$ . Compare $2x^2 + 15x + 25$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $2*25 = 50$ ) and whose sum is $b$ ( $15$ ). $\newline$ We need to find two numbers that multiply to $50$ and add up to $15$ . $\newline$ $10 * 5 = 50$ $\newline$ $10 + 5 = 15$ $\newline$ Two numbers: $10, 5$
Rewrite middle term: Rewrite the middle term $15x$ using the two numbers found in Step $2$ . $2x^2 + 10x + 5x + 25$ Now we have four terms instead of three.
Factor by grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms. $\newline$ $(2x^2 + 10x) + (5x + 25)$ $\newline$ Factor out the greatest common factor from each group. $\newline$ $2x(x + 5) + 5(x + 5)$
Factor common binomial: Factor out the common binomial factor. $\newline$ The common binomial factor is $(x + 5)$ . $\newline$ Factor this out from both groups. $\newline$ $(2x + 5)(x + 5)$