Answer:
B(x) = (x-4)(x² + 4x - 5).
Explanation:
Step 1: Start by dividing the polynomial function by the known factor (x-4) using polynomial long division or synthetic division.
(x³ - 21x + 20) ÷ (x-4)
Step 2: Perform the division and obtain the quotient.
(x³ - 21x + 20) ÷ (x-4) = x² + 4x - 5
Step 3: The quotient obtained, x² + 4x - 5, represents the other linear factor of B(x).
Step 4: Write the original polynomial B(x) as a product of the known factor (x-4) and the other linear factor (x² + 4x - 5).
B(x) = (x-4)(x² + 4x - 5)
So, the polynomial function B(x) = x³ - 21x + 20 can be rewritten as the product of linear factors as B(x) = (x-4)(x² + 4x - 5).