Final answer:
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