Question

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

3x² + 6x – 24

Answer 1

According to the question,

Let p(x) = 3x² + 6x − 24 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) = 3(2)² + 6(2) – 24

= 12 + 12 – 24

= 0

Since, the remainder = zero,

We can say that,

g(x) = x – 2 is factor of p(x) = 3x² + 6x − 24