Determine which of the following polynomial has x – 2 a factor (i) 3

1.	Determine which of the following polynomial has x – 2 a factor (i) 3x2 + 6x – 24 (ii) 4x2+ x – 2
Answer» (i) 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 (ii) According to the question, 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 factor of p(x) = 4x² + x −2

Determine which of the following polynomial has x – 2 a factor (i) 3x2 + 6x – 24 (ii) 4x2+ x – 2

Answer»

(i) 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

(ii) According to the question,

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