Rhea adds the two polynomials 2x³ + 5x − 1 and −2x³ + x² + 4. What is the degree of the sum?

2. Add like terms: (2x³ − 2x³) + x² + 5x + (−1 + 4) = x² + 5x + 3. The x³ terms cancel, so the degree of the sum is 2 — not 3. Adding polynomials can lower the degree.

Rhea adds the two polynomials $2 x^{3} + 5 x - 1$ and $- 2 x^{3} + x^{2} + 4$ . What is the degree of the sum?

Class 9PolynomialsPolynomials

Step-by-Step Solution

Add like terms:

(2 x^{3} - 2 x^{3}) + x^{2} + 5 x + (- 1 + 4) = x^{2} + 5 x + 3

. The

x^{3}

terms cancel, so the degree of the sum is 2 — not 3. Adding polynomials can lower the degree.

Answer: C) 2

Key idea: Naming polynomials by terms and degree

By number of terms:
- **Monomial**: 1 term (e.g.

5 x^{3}

)
- **Binomial**: 2 terms (e.g.

x^{2} + 3

)
- **Trinomial**: 3 terms (e.g.

x^{2} + 2 x + 1

)

By degree:
- **Linear** (degree 1):

3 x - 5

- **Quadratic** (degree 2):

x^{2} - 4

- **Cubic** (degree 3):

2 x^{3} + x - 1

- **Biquadratic** (degree 4):

x^{4} + 1

A polynomial can fit multiple categories.

5 x^{3}

is both a monomial and a cubic.

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Rhea adds the two polynomials 2x3+5x−1 and −2x3+x2+4. What is the degree of the sum?

Step-by-Step Solution

Key idea: Naming polynomials by terms and degree

Master this chapter in 30 minutes a day.

More Class 9 Polynomials practice

Rhea adds the two polynomials $2 x^{3} + 5 x - 1$ and $- 2 x^{3} + x^{2} + 4$ . What is the degree of the sum?