The room has a floor space of 2x^2-15x+7 if the width of the room is (x-7) feet what is the lenght. this is a factoring problem for my algebra worksheet

Question

The room has a floor space of 2x^2-15x+7 if the width of the room is (x-7) feet what is the lenght. this is a factoring problem for my algebra worksheet

Answer 1

2x^2-15x+7

area=length*width

you have to factor 2x^2-15x+7 but you already know one of the factors, (x-7)

(x-7)(    )

(x-7)(2x   ) so far because you need 2x^2

(x-7)(2x 1) so far because you need 7 (you need a +7 and (-)(-)=+)

(x-7)(2x-1)=2x^2-15x+7

the length is (2x-1)

Answer 2

Remember that the floor space (area) of a room is the room's length x width.  We are given the area and the width, so we can plug them in to solve for the length.  

 

2x^2 - 15x + 7 = length * (x-7)

 

Now factor the polynomial on the left as follows:

 

(2x - 1)(x-7)

 

Notice that we have the term (x-7) now on both sides.

 

(2x-1)(x-7) = length * (x-7)

Divide both sides by (x-7) and you are left with:

 

length = (2x-1)