# How do you factor 12x^2-29x+15?

Aug 15, 2016

#### Answer:

$\left(3 x - 5\right) \left(4 x - 3\right)$

#### Explanation:

We are looking for factors of 12 and 15 which add to give 29.
The signs are the same, both negative.

There are some clues...
29 is an odd number which can only be formed from :
odd + even.

The factors of 15 are all odd. This implies that the factors of 12 must not both be even - $2 \times 6$ are not possible.

We are left with $1 \times 12 \mathmr{and} 3 \times 4$

Find the sum of the cross products.

$\text{ "3" "5" } \Rightarrow 4 \times 5 = 20$
$\text{ "4" "3" "rArr 3xx3 = 9 " } 20 + 9 = 29$

The top row is the first bracket.
The bottom row is the second bracket.

$\left(3 x - 5\right) \left(4 x - 3\right)$