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.