How do you factor $10 x^{2} - 8 x - 15 x + 12$ $10x^2 - 8x - 15x + 12$ ?

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How do you factor $10 x^{2} - 8 x - 15 x + 12$ $10x^2 - 8x - 15x + 12$ ?

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Answer 1 · 2018-05-16T13:16:22

$(2 x - 3) (5 x - 4)$ $(2x-3)(5x-4)$

Explanation:

$if the ratios of the coefficients of the first/second terms$ $"if the ratios of the coefficients of the first/second terms"$
$and third/fourth terms are equal we can factor by grouping$ $"and third/fourth terms are equal we can factor by grouping"$

$As they stand this is not the case but rearranging gives$ $"As they stand this is not the case but rearranging gives"$

$10 x^{2} - 15 x - 8 x + 12 \leftarrow factor by grouping$ $10x^2-15x-8x+12larrcolor(blue)"factor by grouping"$

$= 5 x (2 x - 3) - 4 (2 x - 3)$ $=color(red)(5x)(2x-3)color(red)(-4)(2x-3)$

$take out the common factor (2 x - 3)$ $"take out the "color(blue)"common factor "(2x-3)$

$= (2 x - 3) (5 x - 4)$ $=(2x-3)(color(red)(5x-4))$

$\Rightarrow 10 x^{2} - 8 x - 15 x + 12 = (2 x - 3) (5 x - 4)$ $rArr10x^2-8x-15x+12=(2x-3)(5x-4)$

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How do you factor $10 x^{2} - 8 x - 15 x + 12$ $10x^2 - 8x - 15x + 12$ ?

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