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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)

Respuesta :

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

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

Part B: Our polynomial has three terms, so is a trinomial; also, our polynoal only has one variable, [tex]x[/tex], 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.

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 = [tex]\frac{base * height}{2}[/tex]

= 0.5bh

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

area = [tex]\frac{(8x+2)(4x-5)}{2}[/tex]

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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