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$2x^2 -14x+7$

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Factor polynomials

Full solution

Q.

2x^2 -14x+7

Identify coefficients: Step $1$ : Identify coefficients $a$ , $b$ , and $c$ from the quadratic expression $2x^2 - 14x + 7$ . $a = 2$ , $b = -14$ , $c = 7$
Find number pair: Step $2$ : Find two numbers that multiply to $ac$ ( $2\times7=14$ ) and add up to $b$ ( $-14$ ). $\newline$ Possible pairs: $(-2, -12)$ , $(-1, -14)$ $\newline$ Correct pair: $(-2, -12)$ because $-2 \times -12 = 14$ and $-2 + -12 = -14$
Rewrite middle term: Step $3$ : Rewrite the middle term using the numbers found. $2x^2 - 2x - 12x + 7$
Factor by grouping: Step $4$ : Factor by grouping. $\newline$ Group the terms: $2x^2 - 2x$ + $-12x + 7$ $\newline$ Factor out the common factors: $2x(x - 1) - 7(2x - 1)$
Factor common binomial: Step $5$ : Factor out the common binomial. $\newline$ $(2x - 7)(x - 1)$

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