# Can y= 15x^2-x-2  be factored? If so what are the factors ?

Feb 17, 2016

(3x + 1 )(5x - 2 )

#### Explanation:

The standard form of a quadratic function is $y = a {x}^{2} + b x + c$

To factor it , consider the factors of the product ac , which sum to give b.
here a = 15 , b = -1 and c= - 2

the product ac = $15 \times - 2 = - 30 \text{ require factors to sum to - 1 }$

the factors are - 6 and 5 as these also sum to - 1. Now rewrite the function replacing -x by +5x - 6x

hence $15 {x}^{2} + 5 x - 6 x - 2 \text{ and factor the 'pairs'}$

ie $\left[5 {x}^{2} + 5 x\right] \mathmr{and} \left[- 6 x - 2\right]$

$\Rightarrow 5 x \left(3 x + 1\right) \mathmr{and} - 2 \left(3 x + 1\right)$

now there is a common factor of (3x + 1 ) in the 2 terms.
becomes (3x + 1 )( 5x - 2 )

$\Rightarrow 15 {x}^{2} - x - 2 = \left(3 x + 1\right) \left(5 x - 2\right)$