Suppose p(x) is a polynomial of degree n (n ≥ 0), and z; (0 ≤ i ≤n) are a set of distinct. points on the real axis. Is the following relation true? Briefly explain why. p(x) = p[ro] + p[ro, 21] (x − x0) + p[ro, x1, x2] (x − xo)(x − x₁) + ... + p[ro, 1,...,n] (x − xo)(x − x₁)(x - xn-1)

Given the function ƒ (x) = x³ − 3x² + 3x − 1, determine the real zeros and state the multiplicity of any repeated zeros. O { 1 mult. 3} O {1 mult. 2, 1/2} O {0, 2, -1} O {-1 mult. 3}

5. Let the polynomial function g be a function of x. The graph of the polynomial has four zeros at -5, –,0,7. Select all the expressions that could represent g: -4x(x + 5)(4x + 3)(x – 7) -4x(x + 5)(4x +3)(x – 7)² 4x(x – 5)(x +)(x + 7) 42(т + 5) (3а —4) (ӕ — 7) -æ(x + 5)(x +)(x – 7) a. b. C. d. е.

Use the given polynomial function to answer the questions. f (x) = x² (2x – 1)² What is the degree of the polynomial? What is the leading coefficient? Which describes the end behavior of the function? As x → -00, f (x) → -00; as x → 0, f (x) → 0 As x → -, f (x) → ∞; as x → ∞, f (x) → ∞ As x → -0, f (x) → ∞; as x → ∞, f (x) → -00 As x → -0, f (x) → -∞; as x → ∞, f (x) → -∞