How do you factor completely $5 x^{2} - 23 x + 12$ $5x^2 - 23 x + 12$ ?

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How do you factor completely $5 x^{2} - 23 x + 12$ $5x^2 - 23 x + 12$ ?

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Answer 1 · 2016-03-17T20:46:04

Use an AC method and factor by grouping to find:

$5 x^{2} - 23 x + 12 = (5 x - 3) (x - 4)$ $5x^2-23x+12=(5x-3)(x-4)$

Explanation:

We can use an AC method.

Look for a pair of factors of $A C = 5 \cdot 12 = 60$ $AC = 5*12 = 60$ with sum $B = 23$ $B=23$ .

The pair $20, 3$ $20, 3$ works.

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

$5 x^{2} - 23 x + 12$ $5x^2-23x+12$

$= 5 x^{2} - 20 x - 3 x + 12$ $=5x^2-20x-3x+12$

$= (5 x^{2} - 20 x) - (3 x - 12)$ $=(5x^2-20x)-(3x-12)$

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

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

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How do you factor completely $5 x^{2} - 23 x + 12$ $5x^2 - 23 x + 12$ ?

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