Question

Find all zeros of the polynomial P(x) = x3 - 3x2 - 10x + 24 knowing that x = 2 is a zero of the polynomial.

Answer 1

Answer:

• x = 2, x = 4, x = -3

Step-by-step explanation:

Given

• P(x) = x3 - 3x2 - 10x + 24
• One of zeros is x = 2

To find

• All zeros

Solution

x³ - 3x² - 10x + 24 is divisible by x - 2 as one of zeros is 2, then:

• x³ - 2x² - x² + 2x - 12x + 24 =
• (x - 2)(x² - x - 12) =
• (x - 2)( x² - 4x + 3x - 12) =
• (x - 2)(x - 4)(x + 3)

Other zeros are x = 4 and x = -3