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

Question

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.

Answer 1

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 

Answer 2

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

Answer 3

w(w-6) + 1(w-6)

 

Factor out the w-6 from both terms:

= (w-6)(w+1)

Answer 4

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)