Question

(i) For what value of m is x³ – 2mn² + 16 divisible by (x + 2)?

(ii) Show that (2x – 3) is a factor of x + 2x³ – 9x + 12.

Answer 1

(i) Let p(x) = x³ – 2mn² + 16

p(x) will be divisible by (x + 2) if

p(-2)= 0

p(-2) = (-2)³ – 2m(-2)² + 16 

= -8 – 8m + 16 

= – 8m + 8

p(-2) = 0

⇒ -8m + 8 = 0

⇒ 8m = 8

⇒ m = 1

(ii) We know that (2x – 3) will be a factor of x + 2x³ – 9x + 12 

if p(x) on dividing by 2x – 3, leaves  a remainder zero

So, the remainder obtained on dividing p(x) by 2x – 3 is zero.

Hence, (2x – 3) is a factor of x + 2x³ – 9x + 12