How do you factor $6 x^{2} - 25 x + 14$ $6x^2 - 25x + 14$ ?

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How do you factor $6 x^{2} - 25 x + 14$ $6x^2 - 25x + 14$ ?

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Answer 1 · 2016-08-30T18:02:23

$6 x^{2} - 25 x + 14 = (3 x - 2) (2 x - 7)$ $6x^2-25x+14=(3x-2)(2x-7)$

Explanation:

Given:

$6 x^{2} - 25 x + 14$ $6x^2-25x+14$

Use an AC Method:

Look for a pair of factors of $A C = 6 \cdot 14 = 84$ $AC=6*14=84$ which sum to $B = 25$ $B=25$ .

The pair $21, 4$ $21, 4$ works.

Use this pair to split the middle term and factor by grouping:

$6 x^{2} - 25 x + 14$ $6x^2-25x+14$

$= 6 x^{2} - 21 x - 4 x + 14$ $=6x^2-21x-4x+14$

$= (6 x^{2} - 21 x) - (4 x - 14)$ $=(6x^2-21x)-(4x-14)$

$= 3 x (2 x - 7) - 2 (2 x - 7)$ $=3x(2x-7)-2(2x-7)$

$= (3 x - 2) (2 x - 7)$ $=(3x-2)(2x-7)$

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How do you factor $6 x^{2} - 25 x + 14$ $6x^2 - 25x + 14$ ?

1 Answer

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