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.
How do I factor this expression out completely: w(w-6)+w-6
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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
Let's distribute the w...
Let's combine like terms...
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(w-6) + 1(w-6)
Factor out the w-6 from both terms:
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)