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$5x^2+11x-7\div x-4$

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Factor polynomials

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Q.

5x^2+11x-7\div x-4

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $5x^2+11x-7$ . $\newline$ $a = 5$ , $b = 11$ , $c = -7$
Find two numbers: Find two numbers that multiply to $a*c$ ( $5*-7 = -35$ ) and add up to $b$ ( $11$ ). $\newline$ The numbers are $14$ and $-3$ because $14 * -3 = -35$ and $14 + (-3) = 11$ .
Rewrite middle term: Rewrite the middle term $11x$ using the two numbers found, splitting it into $14x$ and $-3x$ . $\newline$ $5x^2 + 14x - 3x - 7$
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(5x^2 + 14x) + (-3x - 7)$
Factor out common factor: Factor out the common factor from each group. $\newline$ $5x(x + \frac{14}{5}) - 1(x + \frac{14}{5})$

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