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the length of a rectangle is (5x2 + 4x - 4) units, and its width is (4x3 - 2x + 6) units.

part a: what is the area of the rectangle? show your work. (5 points)

part b: is the answer for part a an example of polynomials being closed under an operation? justify your answer. (3 points)

part c: what is the degree and classification of the expression obtained in part a?

Part A

The area is 20x5+16x4−26x3+22x2+32x−24 sqaure units

Part B

Yes the answer is polynomial

Part C

The degree is 5

The solution is given in the attached figure

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. So the answer is a polynomial in our case.

The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients. The degree of an expression is the sum of the exponents of the variables that appear in the polynomial, and thus is a non-negative integer. In our case the degree of the polynomial is 5.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.