Question

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

Answer 1

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

Explanation:

The standard form of a quadratic function is `y = ax^2 + bx + 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 xx -2 = - 30 " 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 `15x^2 + 5x - 6x - 2 " and factor the 'pairs'"`

ie `[ 5x^2 + 5x ] and [ - 6x - 2 ]`

`rArr 5x (3x + 1 ) and - 2(3x + 1 )`

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

`rArr 15x^2 - x - 2 = (3x + 1 )(5x - 2 )`