Question

15 POINTS! ALGEBRA HOMEWORK PLEASE HELP ASAP!

1. What is the product of -2x^3 + x - 5 and x^3 - 3x - 4?
Show your work.

2. Is the product of -2x^3 + x - 5 and x^3 - 3x - 4 equal to the product of x^3 - 3x - 4 and -2x^3 + x - 5?
Explain your answer.

Answer 1

Simplify the following:
x^3 - 2 x^3 + x - 3 x - 5 - 4

Grouping like terms, x^3 - 2 x^3 + x - 3 x - 5 - 4 = (-2 x^3 + x^3) + (x - 3 x) + (-5 - 4):
(-2 x^3 + x^3) + (x - 3 x) + (-5 - 4)

x^3 - 2 x^3 = -x^3:
-x^3 + (x - 3 x) + (-5 - 4)

x - 3 x = -2 x:
-x^3 + -2 x + (-5 - 4)

-5 - 4 = -9:
-x^3 - 2 x + -9

Factor -1 out of -x^3 - 2 x - 9:

Answer: -(x^3 + 2 x + 9)

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Yes = (-2x^3 + x - 5)+( x^3 - 3x - 4) = ( x^3 - 3x - 4)+(-2x^3 + x - 5) = True

Proof:
Left side

Simplify the following:
x^3 - 2 x^3 + x - 3 x - 5 - 4

Grouping like terms, x^3 - 2 x^3 + x - 3 x - 5 - 4 = (-2 x^3 + x^3) + (x - 3 x) + (-5 - 4):
(-2 x^3 + x^3) + (x - 3 x) + (-5 - 4)

x^3 - 2 x^3 = -x^3:
-x^3 + (x - 3 x) + (-5 - 4)

x - 3 x = -2 x:
-x^3 + -2 x + (-5 - 4)

-5 - 4 = -9:
-x^3 - 2 x + -9

Factor -1 out of -x^3 - 2 x - 9:
Answer: -(x^3 + 2 x + 9)
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Right Side.

Simplify the following:
x^3 - 2 x^3 + x - 3 x - 5 - 4

Grouping like terms, x^3 - 2 x^3 + x - 3 x - 5 - 4 = (x^3 - 2 x^3) + (-3 x + x) + (-4 - 5):
(x^3 - 2 x^3) + (-3 x + x) + (-4 - 5)

x^3 - 2 x^3 = -x^3:
-x^3 + (-3 x + x) + (-4 - 5)

x - 3 x = -2 x:
-x^3 + -2 x + (-4 - 5)

-4 - 5 = -9:
-x^3 - 2 x + -9

Factor -1 out of -x^3 - 2 x - 9:
Answer: -(x^3 + 2 x + 9)