Form a polynomial whose zeros and degree are given Zeros 8

Form a polynomial whose zeros and degree are given. Zeros: - 8, multiplicity 1; -3, multiplicity2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. f(x) = (Simplify your answer.)

Solution

Form a polynomial whose zeros and degrees are given.
Zeros:-8; degree 3
Each zero, eg, z, contributes a factor (x - z)
-8 is a zero and it shows up 1 times in the polynomial as (x+8) Another zero is -3 and that shows up 2 times as (x+3)²

So our polynomial will be

(x+8).(x+3)²

=(x+8).(x²+6x+9)

= x³+6x²+9x+8x²+48x+72

= x³+14x²+57x+72 is our required equation