Answer:
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.
