Question

A polynomial has x-intercepts of 3, 0, and –1, and passes through the point (1, –8). Which of the following functions could represent this graph? 1. x3 – 2x2 – 3x 2. x2 – 2x – 3 3. 2x2 – 4x – 6 4. 2x3 – 4x2 – 6x

Answer 1

D) 2x3 – 4x2 – 6x

Explanation:

Answer 2

option 4

Explanation:

Given the x- intercepts say x = a, x = b, x - c then the corresponding factors are

(x - a), (x - b), (x - c) and the polynomial is the product of the factors

Here the x- intercepts are x = 3, x = 0, x = - 1, thus the factors are

(x - 3), (x - 0), (x - (- 1) , that is

(x - 3), x and (x + 1) , then

y = ax(x - 3)(x + 1) ← where a is a multiplier

To find a substitute (1, - 8) into the equation

- 8 = a(1 - 3)(1 + 1) = - 4a ( divide both sides by - 4 )

a = 2, thus

y = 2x(x - 3)(x + 1) ← expand factors using FOIL

= 2x(x² - 2x - 3) ← distribute by 2x

= 2x³ - 4x² - 6x