Question

(Score:

of 5 points)
3. Multiply the polynomials (3x² - 4x + 5)(2x³ + 3x² - 4x). Simplify the answer.
Show all work.

Answer 1

To multiply the given polynomials, we use the distributive property and combine like terms. As a result, the simplified answer is 6x^5 + x^4 - 24x^3 + 31x² - 20x.

Step-by-step explanation:

To multiply the two polynomials (3x² - 4x + 5)(2x³ + 3x² - 4x), we can use the distributive property. We multiply each term in the first polynomial by each term in the second polynomial:

First, multiply each term in the first polynomial by 2x³:

2x³ * 3x² = 6x^(3+2) = 6x^5

2x³ * -4x = -8x^(3+1) = -8x^4

2x³ * 5 = 10x³

Next, multiply each term in the first polynomial by 3x²:

3x² * 3x² = 9x^(2+2) = 9x^4

3x² * -4x = -12x^(2+1) = -12x^3

3x² * 5 = 15x²

Finally, multiply each term in the first polynomial by -4x:

-4x * 3x² = -12x^(1+2) = -12x^3

-4x * -4x = 16x^(1+1) = 16x²

-4x * 5 = -20x

We can now add up all the terms to get the simplified answer:

6x^5 - 8x^4 + 10x³ + 9x^4 - 12x^3 + 15x² - 12x^3 + 16x² - 20x

In the simplified form, this becomes:

6x^5 + x^4 - 24x^3 + 31x² - 20x

Learn more about Multiplying polynomials