FIND DEGREE AND LEADING COEFFICIENT OF POLYNOMIALS

For each polynomial, state the degree, the leading coefficient and the constant term.

Problem 1 :

2x³ + x² - x + 3

Solution :

Given polynomial is 2x³ + x² - x + 3

Since, the highest power of 2 is 3.

Therefore, the degree of the given polynomial is 3.

Leading coefficient is 2. And the constant term is 3.

Problem 2 :

x⁵ - x³ + x - 2

Solution :

Given polynomial is x⁵ - x³ + x - 2

Since, the highest power of 1 is 5.

Therefore, the degree of the given polynomial is 5.

Leading coefficient is 1. And the constant term is -2.

Problem 3 :

9x⁴ + x²

Solution :

Given polynomial is 9x⁴ + x² 

Since, the highest power of 9 is 4.

Therefore, the degree of the given polynomial is 4.

Leading coefficient is 9. And the constant term is 0.

Problem 4 :

5 - 2x

Solution :

Given polynomial is 5 - 2x

Since, the highest power of -2 is 1.

Therefore, the degree of the given polynomial is 1.

Leading coefficient is -2. And the constant term is 5.

Problem 5 :

7x⁶

Solution :

Given polynomial is 7x⁶

Since, the highest power of 7 is 6.

Therefore, the degree of the given polynomial is 6.

Leading coefficient is 7. And the constant term is 0.

Problem 6 :

5 - 2x + x²

Solution :

Given polynomial is 5 - 2x + x²

Since, the highest power of 1 is 2.

Therefore, the degree of the given polynomial is 2.

Leading coefficient is 1. And the constant term is 5.

Problem 7 :

9 - x² + x⁴ - x⁶

Solution :

Given polynomial is 9 - x² + x⁴ - x⁶

Since, the highest power of -1 is 6.

Therefore, the degree of the given polynomial is 6.

Leading coefficient is -1. And the constant term is 9.

Problem 8 :

3

Solution :

3 is a single variable. So, no highest power of polynomial.

3 is a constant term.

Problem 9 :

x³ - 2x⁵

Solution :

Given polynomial is x³ - 2x⁵ 

Since, the highest power of -2 is 5.

Therefore, the degree of the given polynomial is 5.

Leading coefficient is -2. And the constant term is 0.

Problem 10 :

√3x² + √2x + 1

Solution :

Given polynomial is √3x² + √2x + 1

Since, the highest power of √3 is 2.

Therefore, the degree of the given polynomial is 2.

Leading coefficient is √3. And the constant term is 1.

Problem 11 :

5x³ + 3x⁴/2

Solution :

Given polynomial is 5x³ + 3x⁴/2

Since, the highest power of 3/2 is 4.

Therefore, the degree of the given polynomial is 4.

Leading coefficient is 3/2. And the constant term is 0.

Problem 12 :

x⁴/3 + x²/2 + 1/5

Solution :

Given polynomial is x⁴/3 + x²/2 + 1/5

Since, the highest power of 1/3 is 4.

Therefore, the degree of the given polynomial is 4.

Leading coefficient is 1/3. And the constant term is 1/5.