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

##### 1 Answer

Feb 17, 2016

(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= - 2the 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 )#