Final answer:
The difference between the polynomials (12x^3+10x+4) and (15x^3+7x^2+12x+9) is -3x^3 - 7x^2 - 2x - 5, found by subtracting terms of the second polynomial from those of the first.
Step-by-step explanation:
The student is asking for the difference between two polynomials (12x^3+10x+4) and (15x^3+7x^2+12x+9). To find this difference, we need to subtract the second polynomial from the first. This means that we will subtract each term of the second polynomial from the corresponding term of the first. If there is no corresponding term, we simply write the term from the first polynomial.
The process is as follows:
- Subtract the x^3 terms: 12x^3 - 15x^3 = -3x^3.
- There is no x^2 term in the first polynomial, so we retain the -7x^2 from the second polynomial.
- Subtract the x terms: 10x - 12x = -2x.
- Subtract the constant terms: 4 - 9 = -5.
Putting it all together, we get the result: -3x^3 - 7x^2 - 2x - 5.