Question 1 Essay Worth 10 points 0702 MC The lengths of two

Question 1 (Essay Worth 10 points) (07.02 MC) The lengths of two sides of a triangle are shown below: Side 1: 3x2 2x 1 Side 2: 9x + 2x2 3 The perimeter of the triangle is 5x3 + 4x2 x 3. Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points) Part B: What is the length of the third side of the triangle? (4 points) Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Question 2 (Essay Worth 10 points) (07.01, 07.06 MC) A rectangle has sides measuring (4x + 5) units and (3x + 10) units. Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. (4 points) Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

Question 3 (Essay Worth 10 points) (07.09 HC) A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading. The spilled sauce is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = r2. Part A: Find the area of the circle of spilled sauce as a function of time, or A[r(t)]. Show your work. (6 points) Part B: How large is the area of spilled sauce after 5 minutes? You may use 3.14 to approximate in this problem. (4 points)

Solution

Part A: the sum of Side 1 and Side 2= 5x^2+7x-4

Part B all you have to do is the same thing, but subtract the sum of side 1 and 2 from the total. 5x^3-0x^3=? 4x^2-5x^2=? -x-7x=? -3-4=?

Part C:The closure property states that one polynomial plus another polynomial is also a polynomial. It is the same for addition, subtraction, multiplication, and division

Question 2:

Well, the area of a rectangle is simply the product of the two sides, in this case, (4x+5)(3x+10) sq.units. Expand the product to get the actual expression. It will be a degree 2 polynomial. Assuming, we are talking about the ring of polynomials with real coefficients, see that the product is also a polynomial with real coefficients so we have closure under multiplication ( can say the same if we are talking about the ring of polynomials with integer or rational coefficients)

Well, multiplying the two expressions goes like this: (4x+5)(3x+10) = 4x*(3x+10) + 5*(3x + 10) = 4x*3x + 4x*10 + 5*3x + 5*10 = 12x2+40x+15x+50 = 12x2+55x+50

Question 3: