How do you factor the expression $15 x^{2} - 14 x + 3$ $15x^2-14x+3$ ?

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How do you factor the expression $15 x^{2} - 14 x + 3$ $15x^2-14x+3$ ?

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Answer 1 · 2016-05-12T22:50:34

$15 x^{2} - 14 x + 3 = (3 x - 1) (5 x - 3)$ $15x^2-14x+3=(3x-1)(5x-3)$

Explanation:

Use an AC method:

Find a pair of factors of $A C = 15 \cdot 3 = 45$ $AC = 15*3 = 45$ with sum $B = 14$ $B=14$ .

The pair $9, 5$ $9, 5$ works.

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

$15 x^{2} - 14 x + 3$ $15x^2-14x+3$

$= 15 x^{2} - 9 x - 5 x + 3$ $=15x^2-9x-5x+3$

$= (15 x^{2} - 9 x) - (5 x - 3)$ $=(15x^2-9x)-(5x-3)$

$= 3 x (5 x - 3) - 1 (5 x - 3)$ $=3x(5x-3)-1(5x-3)$

$= (3 x - 1) (5 x - 3)$ $=(3x-1)(5x-3)$

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How do you factor the expression $15 x^{2} - 14 x + 3$ $15x^2-14x+3$ ?

1 Answer

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