19) The area in square feet of a rectangular carpet is x^2 - 17x+30 Find the dimensions for the

expressions of the length and the width.

The dimensions are x-15 and x-2.

Step-by-step explanation:

The formula for the area of a rectangle is A = l x w, where l is length and w is width.

The area is found by multiplying two numbers OR expressions that represent the length and the width.

If the area is x² - 17x + 30, factoring this will give two expressions for length and width.

When factoring, first check if there is a common factor other than 1 between all of the variables. There is no common factor for this.

We can factor using decomposition.

x² - 17x + 30

Write out the factors for the first and last terms:

Since the middle number is a negative, the right side factors should be negative also.

1 - 30 - 15 - 10 - 6

1 - 1 - 2 - 3 - 5

To find the correct pair of factors, the pairs multiplied diagonally from each side then added together should give the middle number, - 17. (The first term's correct factors can only be 1 and 1).

The correct pairing is:

1 - 15

1 - 2

(1 x - 15) + (1 x - 2) = - 17

The factors for factored form are found by adding brackets around the terms.

(1 - 15)

(1 - 2)

x² - 17x + 30 = (x - 15) (x - 2)

Apply the area formula A = (l) (w).

The dimensions are x-15 and x-2.