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How do I factor this expression out completely: w(w-6)+w-6

I'm having trouble understanding how to factor out this equation.  I've factored out other equations but this one just got me in a blind spot.

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Robert S. | Robert Math PhysicsRobert Math Physics
0
Hi
Question factor w(w-6) +w -6
 
multiply w with the expression inside the perentheses w(w-6) = w*w -6w w*w=w2
 
the total expression becomes w2-6w+w-6
 
combine like terms -6w + w = -5w
 
now the expression is w2-5w-6
 
the question now is what factors will give a match for the middle term of -5 the factor for the w2 is 1 the factors for the -6 term is 6 -1, 3 -2, -2 3, -6 1 the last giving -5 which matches the middle term
 
therefore (w-6)(w+1) is the answer 
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
0
Hi Taylor;
 
w(w-6)+w-6
Let's distribute the w...
w2-6w+w-6
Let's combine like terms...
w2-5w-6
For the FOIL...
FIRST must be (w)(w)=w2
OUTER and INNER must add-up to be -5w
LAST must be (6)(1) or (1)(6) or (2)(3) or (3)(2) and one number must be negative to produce the result of -6.
(w-6)(w+1)
Let's FOIL...
FIRST...(w)(w)=w2
OUTER...(w)(1)=1w=w
INNER...(-6)(w)=-6w
LAST..(-6)(1)=-6
w2+w-6w-6
w2-5w-6

Comments

factor this expression out completely
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
0
w(w-6) + 1(w-6)
 
Factor out the w-6 from both terms:
= (w-6)(w+1)
Tom D. | Very patient Math Expert who likes to teachVery patient Math Expert who likes to te...
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Write it out slowly and combine like terms (ALWAYS a good idea)
 
w(w-6)+w-6  = w^2-6w+w-6 = w^2 -5w -6 = (w-6)(w+1)