The area of a rectangle is represented by x^(2) +9x+18. Find the binomials that could represent the lengths and width of the rectangle. A. (x + 6)(x + 3) B. (x + 3)(x + 3) C. (x…

Question

The area of a rectangle is represented by
`x^(2) +9x+18`. Find the binomials that could represent the lengths and width of the rectangle.

A. (x + 6)(x + 3)
B. (x + 3)(x + 3)
C. (x + 2)(x + 9)
D. (x + 1)(x + 18)

Answer 1

To find the lengths and width of a rectangle represented by the area , we must factor the expression, resulting in (x + 6)(x + 3) which matches option A.

Step-by-step explanation:

The area of a rectangle is given by the expression x2 + 9x + 18. To find the binomials representing the length and width, we factor this quadratic expression.

Factoring means expressing the quadratic as the product of two binomials. We look for two numbers that multiply to 18 and add up to 9. The numbers 6 and 3 meet these criteria, so the factored form of the quadratic is (x + 6)(x + 3). Therefore, binomials that could represent the lengths and width of the rectangle are x + 6 and x + 3, which corresponds to option A.