Final answer:
To add the given polynomials, we combine like terms and write them in standard form. The final answer after adding the polynomials in standard form is 8x^9 + 12x^7 + 2x^3 + 12x^5 - 4x^2 - 32x - 12.
Step-by-step explanation:
To solve the student's question, we need to add the polynomials and write the answer in standard form. We do this by combining like terms, which are terms that have the same variables raised to the same powers.
Let's look at each polynomial separately:
- a) 4x^5 + 6x^7 - 4x^2 - 8x - 3
- b) 2x^3 + 8x^9 - 8x - 3
- c) 6x^7 + 4x^5 - 8x - 3
- d) 4x^5 + 6x^7 - 8x^1 - 3
The combined polynomial after adding (a), (b), (c), and (d) is:
8x^9 + (6x^7 + 6x^7) + 2x^3 + (4x^5 + 4x^5 + 4x^5) - 4x^2 + (8x - 8x - 8x - 8x) - 3 - 3 - 3 - 3
Now, we combine like terms:
8x^9 + 12x^7 + 2x^3 + 12x^5 - 4x^2 - 32x - 12
And this is our final answer in standard form.