How do you factor the expression $12 x^{2} - 5 x - 3$ $12x^2 - 5x - 3$ ?

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How do you factor the expression $12 x^{2} - 5 x - 3$ $12x^2 - 5x - 3$ ?

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Answer 1 · 2016-04-27T19:56:45

$12 x^{2} - 5 x - 3 = (3 x + 1) (4 x - 3)$ $12x^2-5x-3=(3x+1)(4x-3)$

Explanation:

Use an AC method:

Look for a pair of factors of $A C = 12 \cdot 3 = 36$ $AC = 12*3 = 36$ with difference $B = 5$ $B=5$ .

The pair $9, 4$ $9, 4$ works.

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

$12 x^{2} - 5 x - 3$ $12x^2-5x-3$

$= 12 x^{2} - 9 x + 4 x - 3$ $=12x^2-9x+4x-3$

$= (12 x^{2} - 9 x) + (4 x - 3)$ $=(12x^2-9x)+(4x-3)$

$= 3 x (4 x - 3) + 1 (4 x - 3)$ $=3x(4x-3)+1(4x-3)$

$= (3 x + 1) (4 x - 3)$ $=(3x+1)(4x-3)$

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How do you factor the expression $12 x^{2} - 5 x - 3$ $12x^2 - 5x - 3$ ?

1 Answer

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