Question

The area of a rectangular rug is given by the trinomial r^2-8r-33 use factoring​

Answer 1

r²-8r-33 = (r-11)(r+3) where r = 11 , r = -3

Explanation:

We have given the area a rectangular rug.

Area = r²-8r -33

We have to find the value of r.We have to use factorization method.

r²-8r-33

We have to find two numbers whose product is -33r² and sum is -8r

r²-8r-33 = r²-11r+3r-33

r²-8r-33 =r(r-11)+3(x - 11)

r²-8r-33 = (r-11)(r+3)

To find the value of r put (r-11) = 0 or (r+3) = 0

r = 11 or r = -3

Answer 2

Hello!

The answer is:

`r^(2)-8r-33=(r+3)(r-11)`

With:

`r=-3\\r=11`

Why?

Factoring the quadratic expression we have:

We are looking for two possible values that multiplied gives as result -33 and its algebraic sum gives as result -8, so:

`r^(2)-8r-33=(r+3)(r-11)`

Also,

There are two possible values that make the equation equal to zero: -3 and 11

Let's prove by substituting each value:

Substituting -3

`(-3+3)(-3-11)=(0)(-14)=0`

Substituting 11

`(11+3)(11-11)=(14)(0)=0`

So, there are two possible values for r (area):

`r=-3\\r=11`

Have a nice day!