Question

Add.
(x³−2x²+4)+(2x³+x²−2)
Express the answer in standard form.

Answer 1

The sum of the polynomials (x³−2x²+4) and (2x³+x²−2) is found by combining like terms, resulting in the final answer in standard form: 3x³ − x² + 2.

Step-by-step explanation:

To add the polynomials (x³−2x²+4) and (2x³+x²−2), you need to combine like terms. This means adding the coefficients of the terms with the same degree. Here is the step-by-step process:

1. Identify like terms. In these two polynomials, the like terms are x³ terms, x² terms, and constant terms.
2. Add the coefficients of x³ terms: 1x³ + 2x³ = 3x³.
3. Add the coefficients of x² terms: −2x² + 1x² = −x².
4. Add the constant terms: 4 + (−2) = 2.
5. Combine all the like terms for the final answer in standard form: 3x³ − x² + 2.

Thus, the sum of the two polynomials in standard form is 3x³ − x² + 2.