Question

Determine which of the following polynomials has x – 2 a factor:

4x² + x – 2

Answer 1

Let p(x) = 4x² + x − 2 and g(x) = x – 2

g(x) = x – 2

zero of g(x)

⇒ g(x) = 0

x – 2 = 0

x = 2

Therefore, zero of g(x) = 2

So, substituting the value of x in p(x), we get,

p(2) = 4(2)² + 2 − 2

= 16 ≠ 0

Since, the remainder ≠ zero,

We can say that,

g(x) = x – 2 is not a factor of p(x) = 4x² + x − 2