Question

5. Given that x=-2 is a zero of P(x)=2x3 + x² - 1 1x –10, factor

P(x) as a product of its linear factors. Then find the other zeros.

Answer 1

Explanation:

x = -2 is a zero, so x + 2 is a factor of P(x).

Use grouping to factor.

P(x) = 2x³ + x² − 11x − 10

P(x) = 2x³ + 4x² − 3x² − 11x − 10

P(x) = 2x² (x + 2) − (3x² + 11x + 10)

P(x) = 2x² (x + 2) − (x + 2) (3x + 5)

P(x) = (x + 2) (2x² − (3x + 5))

P(x) = (x + 2) (2x² − 3x − 5)

P(x) = (x + 2) (x + 1) (2x − 5)

The other zeros are x = -1 and x = 5/2.