Q1 of 90 Page 29

Find the remainder on dividing the polynomial x4 + x3 -3x2 + 3x + 1 by the following monomial expression:

x-1

We will find remainder using remainder theorem which states that


If a polynomial p(x) is divided by a polynomial x – a then the remainder is p(a)


Let p(x) = x4 + x3 - 3x2 + 3x + 1


x – 1


comparing x – 1 with x – a we have here a = 1


x – 1= 0, x = 1


⇒ p(a) = p(1)


⇒ p(1) = 14 + 13 – 3(1)2 + 3(1) + 1


⇒ p(1) = 1 + 1 – 3 + 3 + 1


⇒ p(1) = 3


Hence the remainder when p(x) is divided by x – 1 is 3


More from this chapter

All 90 →
3

Verify whether the values indicated against the following polynomials are zeroes of the polynomial.

p(x)=3x+2; x= -2/3

 4

Find the zeroes of the following polynomials.

i. p(x)=x-4


ii. p(x)=4x


iii. p(x)=bx, b≠0


iv. p(x)=x+3


v. p(x)=2x-1


vi. p(x)=3x+7


vii. p(x)=cx +d, c≠0, c, d are real numbers.

 1

Find the remainder on dividing the polynomial x4 + x3 -3x2 + 3x + 1 by the following monomial expression:

 1

Find the remainder on dividing the polynomial x4 + x3 -3x2 + 3x + 1 by the following monomial expression:

x + π