Question

Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x2 − 6x + 1 square feet, what is the length of one side of the room? (2 points) (3x + 1) feet (9x − 1) feet (3x − 1) feet (9x + 1) feet

Answer 1

Answer: (3x − 1)

If the area of the room is 9x2 − 6x + 1 square feet, then the length of one side of the room is (3x − 1) feet. The correct answer between all the choices given is the third choice or letter C. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

Answer 2

(3x − 1) feet

Explanation:

To find this, we will factor the polynomial.

We want factors of a*c that sum to b; in this case, we want factors of 9*1 = 9 that sum to -6.

-3(-3) = 9 and -3+-3 = -6; this tells us how we "split up" bx:

9x²-3x-3x+1

Group together the first two and the last two terms:

(9x²-3x)+(-3x+1)

Factor out the GCF of each group. For the first group, this is 3x:

3x(3x-1)+(-3x+1)

The GCF of the second group is -1 (we want the 3x to be positive and the 1 to be negative so we factor out a negative):

3x(3x-1)-1(3x-1)

The GCF of the two groups is now (3x-1):

(3x-1)(3x-1)

This means the side length if 3x-1 feet.