How do you factor $3 x^{2} - 7 x + 4$ $3x^2-7x+4$ by grouping?

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How do you factor $3 x^{2} - 7 x + 4$ $3x^2-7x+4$ by grouping?

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Answer 1 · 2017-01-19T00:20:08

$3 x^{2} - 7 x + 4 = (3 x - 4) (x - 1)$ $3x^2-7x+4 = (3x-4)(x-1)$

Explanation:

Note that $7 = 3 + 4$ $7 = 3+4$ , so we can split the middle term as $- 3 x - 4 x$ $-3x-4x$ to be able to factor by grouping:

$3 x^{2} - 7 x + 4 = 3 x^{2} - 3 x - 4 x + 4$ $3x^2-7x+4 = 3x^2-3x-4x+4$

$3 x^{2} - 7 x + 4 = (3 x^{2} - 3 x) - (4 x - 4)$ $color(white)(3x^2-7x+4) = (3x^2-3x)-(4x-4)$

$3 x^{2} - 7 x + 4 = 3 x (x - 1) - 4 (x - 1)$ $color(white)(3x^2-7x+4) = 3x(x-1)-4(x-1)$

$3 x^{2} - 7 x + 4 = (3 x - 4) (x - 1)$ $color(white)(3x^2-7x+4) = (3x-4)(x-1)$

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How do you factor $3 x^{2} - 7 x + 4$ $3x^2-7x+4$ by grouping?

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