Factor the trinomial: 2x^(2)+7x+5 Answer:

Identify trinomial: Identify the trinomial to be factored, which is 2x^2 + 7x + 5.Find suitable numbers: Look for two numbers that multiply to give the product of the coefficient of x^2 term (which is 2) and the constant term (which is 5), and add up to the coefficient of the x term (which is 7).Determine numbers: The two numbers that fit the criteria from Step 2 are 5 and 2, since (5)(2) = 10 and 5 + 2 = 7.Rewrite middle term: Write the middle term (7x) as the sum of two terms using the numbers found in Step 3: 5x + 2x. 2x^2 + 7x + 5 becomes 2x^2 + 5x + 2x + 5.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together: (2x^2 + 5x) + (2x + 5).Factor out common factor: Factor out the greatest common factor from each group. From the first group, factor out x, and from the second group, factor out 1. x(2x + 5) + 1(2x + 5).Final factored form: Since both groups contain the common factor (2x + 5), factor this out to get the final factored form. (2x + 5)(x + 1).

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Q. Factor the trinomial:

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2 x^{2}+7 x+5

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Answer:

Identify trinomial: Identify the trinomial to be factored, which is $2x^2 + 7x + 5$ .
Find suitable numbers: Look for two numbers that multiply to give the product of the coefficient of $x^2$ term (which is $2$ ) and the constant term (which is $5$ ), and add up to the coefficient of the $x$ term (which is $7$ ).
Determine numbers: The two numbers that fit the criteria from Step $2$ are $5$ and $2$ , since $(5)(2) = 10$ and $5 + 2 = 7$ .
Rewrite middle term: Write the middle term $7x$ as the sum of two terms using the numbers found in Step $3$ : $5x + 2x$ . $2x^2 + 7x + 5$ becomes $2x^2 + 5x + 2x + 5$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together: $(2x^2 + 5x) + (2x + 5)$ .
Factor out common factor: Factor out the greatest common factor from each group. From the first group, factor out $x$ , and from the second group, factor out $1$ . $x(2x + 5) + 1(2x + 5)$ .
Final factored form: Since both groups contain the common factor $(2x + 5)$ , factor this out to get the final factored form. $(2x + 5)(x + 1)$ .