Question

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

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

Answer 1

The CORRECT answer is -2x^6 + 7x^4 + 3x^3 – 3x^2 + 11x + 20

Explanation:

I go to k12 and all the other answers are incorrect. I had this on my test.

MY WORK:

-2x^6 + 6x^4 + 8x^3 + x^4 – 3x^2 – 4x – 5x^3 + 15x + 20

= -2x^6 + 7x^4 + 3x^3 – 3x^2 + 11x + 20

b) Yes, it would be equal because of the rule of the commutative property. (basically, the order in which you multiply won’t matter.)

Answer 2

For this case we must find the product of the following expressions:
`(-2x ^ 2 + x-5) (x ^ 3-3x-4) =`

We must apply distributive property, that is, multiply each term:

We must bear in mind that:

`+ * - = -\\- * - = +`

`-2x ^ {2 + 3} + 6x^(2 + 1) + 8x ^ 2 + x^(3 + 1) -3x^(1 + 1) -4x-5x ^ 3 + 15x + 20 =\\-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20`

If we multiply
`(x ^ 3-3x-4) (- 2x ^ 2 + x-5)` we would obtain the same result according to the commutative property of the multiplication:

`a * b = b * a`

Answer:

`-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20`