How do you factor the expression #2x^2 + 5x - 18#?

1 Answer
Dec 23, 2015

#(x+9/2)*(x-2)#

Explanation:

first make sure the coefficient of #x^2# is 1
you can factorize a quadratic polynomial in the form:
#x^2+#(sum of two numbers)#x+#(product of two numbers)
let the two numbers be #a,b#
so, from the equation, we have
#a+b = 5/2# #&# #a*b = -18/2 = -9#

solve this 2 equation 2 unknown by substituting either #a=-9/b# or #b=-9/a# into the eq #a+b=5/2#
on solving you get the two numbers #a# & #b# as #9/2,-2#
now, you can write:
#x^2+(-2+9/2)x+(-2*9/2)#
#x^2-2x+9/2x-9#
#x(x-2)+9/2(x-2)#
#(x-2)*(x+9/2)#