How do you factor #2m^2 - 11m + 15#?

2 Answers
Mar 7, 2018

Answer:

#(m-3)(2m-5)#

Explanation:

Here's a way to do it...
#2m^2-11m+15#
Multiply the squared value with 15
#m^2-11m+30#
Factor normally...
#(m-6)(m-5)#
divide both values by 2
#(m-3)(2m-5)#
5/2 won't be a whole number, so move that number before the #m#

Mar 7, 2018

Answer:

(2m - 5)(m - 3)

Explanation:

Use the new AC Method (Socratic Search)
#f(m) = 2m^2 - 11m + 15 =# a(m + p)(m + q)
Converted trinomial:
#f'(m) = m^2 - 11m + 30 =# (m + p')(m + q')
Find p' and q', knowing the sum (-11) and the product (30).
They are: p' = - 5, and q' = - 6
Back to f(m) --> #p = (p')/a = - 5/2#, and #q = -6/2 = - 3#.
Factored form:
# f(m) = 2(m - 5/2)(m - 3) = (2m - 5)(m - 3)#