Find the zeros of the polynomial function and state the multiplicity of each. f(x) = 5(x + 6)2(x - 6)3

Zeroes: ± 6

Step-by-step explanation:

The given polynomial is: .

To find the zeroes of the polynomial we equate it to zero.

⇒

⇒

⇒ x = -6 and x = +6. They are the zeroes of the polynomial.

Since is a quadratic equation it will have two roots. Therefore, the roots are x = -6, -6.

Multiplicity of a root is the number of times the root appears as the solution for the equation.

This makes x = -6 as root with multiplicity two.

Similarly, will have three roots.

∴ x = +6, +6 , +6

x = +6 is a root with multiplicity three.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.