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olga_2 [115]
3 years ago
6

PLSSS HELP. WILL MARK BRAINLIEST. A rectangle has sides measuring (6x + 4) units and (2x + 11) units. Part A: What is the expres

sion that represents the area of the rectangle? Show your work. (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)
Mathematics
1 answer:
Leni [432]3 years ago
4 0

Answer:

Below.

Step-by-step explanation:

Part A: (6x+4)(2x+11)=12x^2+66x+8x+44=12x^2+74x+44

Part B: Degree = 2, Classification = Quadratic

Part C: The polynomial is closed because it is multiplied. You CANNOT close under division.

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What is the completely factored form of f(x)=x3+5x2+4x−6?
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f(x)=x^3+5x^2+4x-6
f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)

Synthetic division yields

-3  |  1   5   4   -6
.    |      -3  -6    6
- - - - - - - - - - - - -
.    |  1   2  -2    0

which translates to

\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2

with remainder 0. Now by the quadratic formula,

x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3

and so

f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))
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