Solved Problems of Polynomial Function

Let’s solve some problems on Polynomial functions.

Problem 1: Identify whether the function is a polynomial function or not.

• Q(x) = 5x^-9 + 2
• P(x) = 2x^1/2 + 3
• F(x) = 4x³ + 7

Solution:

• Q(x) = 5x^-9 + 2 is not a polynomial function as it has negative exponent.
• P(x) = 2x^1/2 + 3 is not a polynomial function as it has fractional exponent.
• F(x) = 4x³ + 7 is a polynomial function as it has positive exponent.

Problem 2: Find the zeros of the polynomial function, P(x) = 3x – 15.

Solution:

To find the roots for the polynomial function we have to equate it to 0.

P(x) = 0

⇒ 3x – 15 = 0

⇒ 3x = 15

⇒ x = 5

The root of polynomial function P(x) = 3x -15 is 5.

Problem 3: Find the zeros of the polynomial function, P(x) = x² + 5x + 6.

Solution:

To find the roots for the polynomial function we have to equate it to 0.

P(x) = 0

x² + 5x + 6 = 0

⇒ x² + 3x + 2x + 6 = 0

⇒ x(x+3) + 2(x + 3) = 0

⇒ (x + 3) (x + 2) = 0

⇒ x = -2, -3

The roots of polynomial function P(x) = x² + 5x + 6 are -3 and -2.

Problem 4: Find the zeros of the polynomial function, P(x) = x³ – 5x² – x + 5.

Solution:

To find the roots for the polynomial function we have to equate it to 0.

P(x) = 0

x³ – 5x² – x + 5 = 0

⇒ x²(x – 5) -1(x – 5) = 0

⇒ (x² – 1) (x – 5) = 0

⇒ (x – 1) (x + 1) (x – 5) = 0

⇒ x = 1, -1, 5

The roots of polynomial function P(x) = x³ – 5x² – x + 5 are 1, -1, 5.

Polynomial Functions are functions consisting of many algebraic terms including constants, variables of different degrees, coefficients, and positive exponents. The degree of the polynomial function is the highest exponent of the variable.

In this article, we will learn about Polynomial Functions, their examples, the degree of polynomial functions, etc. We will also learn about the types of polynomial functions, their graphs, the roots of polynomial functions, and how to identify whether the function is a polynomial function or not.