What is the simplified expression for its length?

Question

The area of a rectangle is x²+6x-16. It’s width is x-2. What is the simplified expression for its length?

Answer 1

You already know x+2 is going to be part of the factor

So x^2+6x-16 = (x-2)(×??)

Make a list of 2 #s that multiply to give -16 and we will position the minus sign to get the middle term (+6x)

Such as:

16 = 2 x 8 or 16 x 1 or 4 x

Since it is really -16, we can get there by multiplying

-2 x 8

2 x -8

16 x -1

-16 x 1

4 x -4

Looks like to get +6x...we must use -2 x 8 and add those two numbers

-2 +8 =6

So -2x + 8x = 6x ( the + sign is understood to be there when not written in).

So the 2 factors for :

x^2+6x-16 are (x-2) and (x+8)

So width is x - 2 and length is x +8