Question

By remainder theorem, find the remainder when, p(x) is divided by g(x) where
(i) p(x) = x - 2x2 - 4x - 1; g(x)= x + 1
(ii) p(x) = 4x - 12x + 14x – 3; 8(x) = 2x - 1
(iii) p(x) = x - 3x + 4x + 50; 8(x)= x - 3​

Answer 1

Answer:

by using remainder theorem, we get following remainders-

Step-by-step explanation:

(i)p(x) = $x - 2x^{2} -4x -1$

       ⇒$2x^{2} -3x -1$

  g(x) = x + 1

        ⇒x = -1

$2(-1)^{2} - 3(-1) -1$

2×1 +3 -1

2+2 = 4

∴ Remainder = 4

(ii)p(x) = $4x - 12x + 14x -3$

        ⇒$6x -3$

  g(x) = $2x-1$

        ⇒x = $\frac{1}{2}$

$6(\frac{1}{2} ) - 3$

$3 - 3$ = 0

∴ Remainder = 0

(iii)p(x) = $x-3x+4x+50$

          ⇒$2x +50$

   g(x) = x - 3

         ⇒ x = 3

2(3) + 50

6 + 50 = 56

∴ Remainder = 56