Factor the trinomial: 2x^(2)+7x+6 Answer:

Identify a, b, c: Identify a, b, and c in the trinomial 2x^2 + 7x + 6. Compare 2x^2 + 7x + 6 with ax^2 + bx + c. a = 2 b = 7 c = 6Find two numbers: Find two numbers whose product is a*c (2*6 = 12) and whose sum is b (7). We need to find two numbers that multiply to 12 and add up to 7. The numbers 3 and 4 satisfy these conditions because: 3 * 4 = 12 3 + 4 = 7Rewrite middle term: Rewrite the middle term (7x) using the two numbers found in Step 2. We can express 7x as 3x + 4x. So, the trinomial becomes: 2x^2 + 3x + 4x + 6Factor by grouping: Factor by grouping. Group the terms into two pairs: (2x^2 + 3x) + (4x + 6) Factor out the greatest common factor from each pair: x(2x + 3) + 2(2x + 3)Factor out common binomial: Factor out the common binomial factor. The common binomial factor is (2x + 3). The factored form is: (x + 2)(2x + 3)

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Q. Factor the trinomial:

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2 x^{2}+7 x+6

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the trinomial $2x^2 + 7x + 6$ . Compare $2x^2 + 7x + 6$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $2*6 = 12$ ) and whose sum is $b$ ( $7$ ). $\newline$ We need to find two numbers that multiply to $12$ and add up to $7$ . $\newline$ The numbers $3$ and $4$ satisfy these conditions because: $\newline$ $3 * 4 = 12$ $\newline$ $3 + 4 = 7$
Rewrite middle term: Rewrite the middle term $7x$ using the two numbers found in Step $2$ . $\newline$ We can express $7x$ as $3x + 4x$ . $\newline$ So, the trinomial becomes: $\newline$ $2x^2 + 3x + 4x + 6$
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $\newline$ $(2x^2 + 3x) + (4x + 6)$ $\newline$ Factor out the greatest common factor from each pair: $\newline$ $x(2x + 3) + 2(2x + 3)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ The common binomial factor is $(2x + 3)$ . $\newline$ The factored form is: $\newline$ $(x + 2)(2x + 3)$