Question

Match the polynomial with its degree and number of terms. (5 points)

A. -4x^2 + 11
B. X^5 + 3x^2 + 12x - 11
C. X^4 + 8x^3 - 2x^2 + 8x - 5
D. 6x^3
E. X 1/2 - 3x + 5


1. 1 term, degree 3
2. 5 terms; degree 4
3. Not a polynomial
4. 4 terms; degree 5
5. 2 terms; degree 2

Answer 1

Let's analyze each polynomial and match it with the appropriate degree and number of terms:

A. \(-4x^2 + 11\)
- **Degree**: 2 (highest exponent is 2)
- **Number of terms**: 2 (terms are \(-4x^2\) and \(11\))
- **Match**: 5. 2 terms; degree 2

B. \(x^5 + 3x^2 + 12x - 11\)
- **Degree**: 5 (highest exponent is 5)
- **Number of terms**: 4 (terms are \(x^5\), \(3x^2\), \(12x\), and \(-11\))
- **Match**: 4. 4 terms; degree 5

C. \(x^4 + 8x^3 - 2x^2 + 8x - 5\)
- **Degree**: 4 (highest exponent is 4)
- **Number of terms**: 5 (terms are \(x^4\), \(8x^3\), \(-2x^2\), \(8x\), and \(-5\))
- **Match**: 2. 5 terms; degree 4

D. \(6x^3\)
- **Degree**: 3 (highest exponent is 3)
- **Number of terms**: 1 (the single term is \(6x^3\))
- **Match**: 1. 1 term, degree 3

E. \(x^{1/2} - 3x + 5\)
- **Degree**: \(1/2\) (which is not an integer; hence it's not a polynomial)
- **Match**: 3. Not a polynomial

So the final matches are:
- A → 5. 2 terms; degree 2
- B → 4. 4 terms; degree 5
- C → 2. 5 terms; degree 4
- D → 1. 1 term, degree 3
- E → 3. Not a polynomial