# How To Solve Polynomial Equations

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

When P (x) = 0         … (1)
Where P (x) is a polynomial expression then the equation (1) is known as a polynomial equation with variable x of        highest power n where n = 0, 1, 2, 3, …, n.

Examples of polynomial expression: -
·         x^2 + 8 x + 16 = 0
·         (x – 1) ( x^3 – 6 x^2 + 9 x) = 0
·         x^2 – x = 0
·         x^5 + 6 x^4 + 4 x^2 – 4 x + 8 = 0

Question 1: - Solve the following polynomial equation and find the value of x.

Solution: -
i)             Factorize the L.H.S. polynomial expression
X^2 + 8 x + 16
= x^2 + 2 * x * 4 + (4)^2
= (x + 4) ^2

ii)          Now write the L.H.S.  expression equal to zero then solve and find the value of x.
(x + 4) ^2 = 0
X + 4 = 0
X = - 4
Therefore x = - 4

Question 2: - If (x – 1) ( x^3 – 6 x^2 + 9 x) = 0, find x.

Solution: -
(x – 1) (x^3 – 6 x^2 + 9 x) = 0
(x – 1) {x (x ^2 – 6 x + 9)} = 0
X (x – 1) (x ^2 – 2 * x * 3 + 3 ^2) = 0
X (x – 1) (x ^2 – 3) ^2 = 0
Therefore x = 0
X – 1 = 0,       hence x = 1
(x ^2 – 3) ^2 = 0, or, x – 3 = 0,         hence x = 3
Answer: - Therefore x = 0, 1, 3, 3