Question

Verify that 2 is a zero of the polynomial x³ + 4x² – 3x – 18.

Answer 1

Given: Let f(x) = x³ + 4x² – 3x – 18. Verify x = 2 is a zero.

f(2) = 2³ + 4(2²) − 3(2) – 18 

= 8 + 4 × 4 – 6 – 18 

= 8 + 16 – 6 – 18

= 24 – 24

= 0

f(2) = 0, so 2 is a zero of f(x); equivalently (x – 2) is a factor the corresponding quotient is x² + 5x + 6.