How do you factor the quadratics #6x^2-x-2# and #x^2-7x+12# ?
1 Answer
Explanation:
In order to find the appropriate split of the middle terms in each of these quadratics, we can use an AC method:
Example 1
Given:
#6x^2-x-2#
look for a pair of factors of
The pair
Use this pair to split the middle term and factor by grouping:
#6x^2-x-2 = (6x^2-4x)+(3x-2)#
#color(white)(6x^2-x-2) = 2x(3x-2)+1(3x-2)#
#color(white)(6x^2-x-2) = (2x+1)(3x-2)#
So this quadratic has zeros
Example 2
Given:
#x^2-7x+12#
look for a pair of factors of
The pair
Use this pair to split the middle term and factor by grouping:
#x^2-7x+12 = (x^2-4x)-(3x-12)#
#color(white)(x^2-7x+12) = x(x-4)-3(x-4)#
#color(white)(x^2-7x+12) = (x-3)(x-4)#
So this quadratic has zeros