Question

A rectangle has a height of 6k³ + 6 and a width of 2k² + 4k + 5. Express the area of the entire rectangle. Your answer should be a polynomial in standard form.

a) 12k⁵ + 48k⁴ + 72k³ + 36k² + 60k + 30
b) 12k⁵ + 24k⁴ + 36k³ + 18k² + 30k + 15
c) 12k⁵ + 48k⁴ + 72k³ + 36k² + 60k + 25
d) 12k⁵ + 24k⁴ + 36k³ + 18k² + 30k + 25

Answer 1

The area of the rectangle is 12k⁵ + 24k⁴ + 36k³ + 18k² + 30k + 15.

Step-by-step explanation:

The area of a rectangle is found by multiplying its width by its height. In this case, the height of the rectangle is 6k³ + 6 and the width is 2k² + 4k + 5.

To find the area, we need to multiply these expressions:

Area = (6k³ + 6)(2k² + 4k + 5)

To simplify, we can use the distributive property:

Area = 6k³(2k² + 4k + 5) + 6(2k² + 4k + 5)

Now, we can further simplify:

Area = 12k⁵ + 24k⁴ + 36k³ + 18k² + 30k + 15

Therefore, the area of the rectangle is represented by the polynomial 12k⁵ + 24k⁴ + 36k³ + 18k² + 30k + 15.