Question

PLEASE SHOW ALL WORK!!!

Answer 1

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.

Answer 2

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.