Question

What should be subtracted from the polynomial 2x³ + 5x² - 11x - 10 so that ( 2x + 7 ) is a factor ? ​

Answer 1

Let a would be subtracted-:

 As 2x - 3 is a factor, using factor theorem,

  for x = 3/2 :

⇒ 2x³ - 5x² + 5x - a = 0

⇒ 2(3/2)³ - 5(3/2)² + 5(3/2) = a

⇒ 2(27/8) - 5(9/4) + 15/2 = a

⇒ (27/4) - (45/4) + (15/2) = a

⇒ ( 27 - 45 + 30 )/4= a

⇒ 12 / 4 = a

⇒ 3 = a

   Hence 3 should be subtracted