Final answer:
To answer the student's question regarding the multiplication of polynomials (3x^4 - 2x + 1) and (2x + 3), each term from the first polynomial is distributed to each term of the second polynomial and then like terms are combined. The final simplified answer is 6x^5 + 9x^4 - 4x^2 - 4x + 3.
Step-by-step explanation:
The student has presented the multiplication of two polynomials: (3x4 - 2x + 1) and (2x + 3).
To multiply polynomials, we distribute each term of the first polynomial by each term of the second polynomial. This is an application of the distributive property of multiplication over addition, also known as the FOIL (First, Outer, Inner, Last) method in the case of binomials.
Here's a step-by-step multiplication:
- Multiply 3x4 by 2x to get 6x5
- Multiply 3x4 by 3 to get 9x4
- Multiply -2x by 2x to get -4x2
- Multiply -2x by 3 to get -6x
- Multiply 1 by 2x to get 2x
- Multiply 1 by 3 to get 3
Combine like terms:
The answer is 6x5 + 9x4 - 4x2 - 4x + 3.