Question

connecting concepts
write a polynomial that
represents the area of the
shaded region.

$x + 5$
$2x - 9$

area: \square

Explanation:

Step1: Recall rectangle area formula

Area = length × width

Step2: Substitute given expressions

$\text{Area} = (2x - 9)(x + 5)$

Step3: Expand using distributive property

$\text{Area} = 2x(x + 5) - 9(x + 5)$

Step4: Compute each term

$\text{Area} = 2x^2 + 10x - 9x - 45$

Step5: Combine like terms

$\text{Area} = 2x^2 + (10x - 9x) - 45$

Answer:

$2x^2 + x - 45$