How do you factor the expression # 6x^2 - 23x + 15#?
1 Answer
Explanation:
Use an AC method:
Find a pair of factors of
The pair
Use this pair to split the middle term and factor by grouping:
#6x^2-23x+15#
#=6x^2-18x-5x+15#
#=(6x^2-18x)-(5x-15)#
#=6x(x-3)-5(x-3)#
#=(6x-5)(x-3)#
Alternatively, you can complete the square and use the difference of squares identity:
#a^2-b^2=(a-b)(a+b)#
with
I will multiply by
#24(6x^2-23x+15)#
#=144x^2-552x+360#
#=(12x)^2-2(12x)(23)+360#
#=(12x-23)^2-23^2+360#
#=(12x-23)^2-529+360#
#=(12x-23)^2-169#
#=(12x-23)^2-13^2#
#=((12x-23)-13)((12x-23)+13)#
#=(12x-36)(12x-10)#
#=(12(x-3))(2(6x-5))#
#=24(x-3)(6x-5)#
Dividing both ends by
#6x^2-23x+15 = (x-3)(6x-5)#