PLEASE SHOW ALL WORK!!! The base of a triangle measures (8x + 2) units and the height measures (4x − 5) units. Part A: W

Question

PLEASE SHOW ALL WORK!!!
The base of a triangle measures (8x + 2) units and the height measures (4x − 5) units.

Part A: What is the expression that represents the area of the triangle? Show your work to receive full credit. (4 points) Hint: Area = 0.5bh

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)

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    0
    2021-09-09T17:39:18+00:00

    Part A: We know that the equation for finding the area of a triangle is A=.0.5(base)(height)=0.5bh; we also know that base=(8x+2) and height=(4x-5), so the only thing we need to do is replacing those values into our Area equation and solve for x:
    A=0.5(8x+2)(4x-5)
    A=0.5(32 x^{2} -40x+8x-10)
    A=0.5(32 x^{2} -32x-10)
    A=16 x^{2} -16x-5
    Now the only thing left is factor the quadratic polynomial:
    A=(4x+1)(4x-5)

    W can conclude that the area of our triangle is A=(4x+1)(4x-5)

    Part B: Our polynomial has three terms, so is a trinomial; also, our polynoal only has one variable, x, and the largest exponent of that variable is 2; therefore is a degree 2 polynomial. In summary, we have a trinomial of degree 2. 

    Part C: Part A demonstrate the closure property of polynomials because after multiplying tow polynomials we obtained another polynomial.

    0
    2021-09-09T17:39:34+00:00

    Part A:

    As given,

    Base of the triangle = 8x + 2 units

    Height of the triangle = 4x − 5 units

    Formula to find area of a triangle = \frac{base * height}{2}

    = 0.5bh

    we have been given base and height, so the area becomes,

    area = \frac{(8x+2)(4x-5)}{2}

    area = 0.5(8x+2)(4x-5)

    = 0.5(32x²-32x-10)

    = 16x²-16-5

    after factoring it, we get

    area = (4x-5)(4x+1) units.

    Part B:

    It is a degree 2 polynomial as the polynomial has one variable that is x, and the largest exponent of that variable is 2.

    Part C:

    Part A demonstrates the closure property of polynomials because after multiplying two polynomials we get another polynomial.

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