How do you factor the expressions #x^2+7x-18#?

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Answer 1 · 2018-05-12T16:14:47

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

Given: #x^2+7x-18#.

Split the middle term.

#=>x^2+9x-2x-18#.

Factor by each side.

#=>x(x+9)-2(x+9)#.

#=>(x+9)(x-2)#

Answer 2 · 2018-05-12T16:16:49

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

#"since the coefficient of the "x^2" term is 1 then"#

#"the factors of - 18 which sum to + 7 are + 9 and - 2"#

#rArrx^2+7x-18=(x+9)(x-2)#

Answer 3 · 2018-05-12T16:21:20

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

With this type of quadratic, we need to find a number that adds to make #7#, but multiplies to make #-18#:

We can start by listing the factors of #18#:

#-18 and 1#

#-1 and 18#

#-9 and 2#

#-2 and 9#

#-6 and 3#

#-3 and 6#

#9+(-2)=7# #lArr "therefore this combination will work"#

Place in double brackets:

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

We can check by expanding:

#(x+9)(x-2)=x^2-2x+9x-18#

#rArr x^2+7x-18#