Question

Help:) Factor f(x) = 4x^3+ 23x^2- 70x + 16 into linear factors given that - 8 is a zero of f(x).

Answer 1

(x + 8)(x - 2)(4x - 1)

Explanation:

Given that x = - 8 is a zero then (x + 8) is a factor

Divide f(x) by (x + 8) using Synthetic division

- 8 | 4 23 - 70 16

↓ - 32 72 - 16

---------------------------------

4 - 9 2 0

Quotient = 4x² - 9x + 2 = (x - 2)(4x - 1)

Thus

f(x) = (x + 8)(x - 2)(4x - 1)