Answer:
The answer to your question is (x₁ - 4)(x₂ - 9)(x₃)(x₄ +4)
Step-by-step explanation:
Data
zeros of a polynomial = 4, 9, 0, -1
Process
1.- Equal each root to zero
x₁ = 4 x₂ = 9 x₃ = 0 x₄ = -1
x₁ - 4 = 0 x₂ - 9 = 0 x₃ = 0 x₄ + 1 = 0
2.- Write the terms together
(x₁ - 4)(x₂ - 9)(x₃)(x₄ +4)
3.- Expand to check the answer
(x - 4)(x - 9) = x² -13x + 36
(x² -13x + 36)(x) = x³ - 13x² + 36x
(x³ - 13x² + 36x)(x + 4) = x⁴ - 13x³ + 36x² + 4x³ - 52x² + 144x
= x⁴ - 9x³ - 16x² + 144
