How To Solve Polynomial Equations Online Tutoring

How To Solve Polynomial Equations Online Tutoring 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