Factor completely. 2x^(2)+9x-35 Answer:

Identify quadratic expression: Identify the quadratic expression to be factored. The given expression is 2x^2 + 9x - 35.Find suitable numbers: Look for two numbers that multiply to give the product of the coefficient of x^2 (which is 2) and the constant term (which is -35), and add up to the coefficient of x (which is 9). The product of the coefficient of x^2 and the constant term is 2 * (-35) = -70. We need two numbers that multiply to -70 and add up to 9. The numbers 14 and -5 satisfy these conditions because 14 * (-5) = -70 and 14 + (-5) = 9.Rewrite middle term: Rewrite the middle term (9x) using the two numbers found in the previous step. The expression 2x^2 + 9x - 35 can be rewritten as 2x^2 + 14x - 5x - 35.Factor by grouping: Factor by grouping. Group the terms to factor common terms out of each group. (2x^2 + 14x) - (5x + 35) Factor out 2x from the first group and -5 from the second group. 2x(x + 7) - 5(x + 7)Factor out common binomial: Factor out the common binomial factor (x + 7). The expression now becomes (2x - 5)(x + 7).

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Algebra 2

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Q. Factor completely.

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2 x^{2}+9 x-35

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Answer:

Identify quadratic expression: Identify the quadratic expression to be factored. $\newline$ The given expression is $2x^2 + 9x - 35$ .
Find suitable numbers: Look for two numbers that multiply to give the product of the coefficient of $x^2$ (which is $2$ ) and the constant term (which is $-35$ ), and add up to the coefficient of $x$ (which is $9$ ). $\newline$ The product of the coefficient of $x^2$ and the constant term is $2 \times (-35) = -70$ . $\newline$ We need two numbers that multiply to $-70$ and add up to $9$ . $\newline$ The numbers $14$ and $2$ $0$ satisfy these conditions because $2$ $1$ and $2$ $2$ .
Rewrite middle term: Rewrite the middle term $9x$ using the two numbers found in the previous step. $\newline$ The expression $2x^2 + 9x - 35$ can be rewritten as $2x^2 + 14x - 5x - 35$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms to factor common terms out of each group. $\newline$ $(2x^2 + 14x) - (5x + 35)$ $\newline$ Factor out $2x$ from the first group and $-5$ from the second group. $\newline$ $2x(x + 7) - 5(x + 7)$
Factor out common binomial: Factor out the common binomial factor $(x + 7)$ . The expression now becomes $(2x - 5)(x + 7)$ .