Olympiad – Class IX – Mathematics - Polynomials

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Question - 1

Write the degree of the polynomial 0.

  • A 1
  • B 0
  • C N
  • D Not defined

Question - 2

If the quotient is 3x2 - 2x + 1, remainder is 2x - 5 and divisor is x + 2, what is the dividend?

  • A 3x3- 4x2+ x- 3
  • B 3x3- 4x2- x + 3
  • C 3x3 + 4x2- x+ 3
  • D 3x3 + 4x2- x- 3

Question - 3

If (x - 2) is one factor of x2+ ax - 6 = 0 and x2- 9x + b = 0, find a + b.

  • A 15
  • B 13
  • C 11
  • D 10

Question - 4

Given P = Product of x2y and \(\frac { x }{ y } \) and Q = Quotient obtained when x2 is divided by D. If P = Q,what is the value of D?

  • A 0
  • B 1
  • C x
  • D \(\frac { 1 }{ x } \)

Question - 5

Which of the following is one of the factors of a3+ 8b3 - 64c3 + 24abc?

  • A a + 2b - 4c
  • B a - 2b + 4c
  • C a + 2b + 4c
  • D a - 2b - 4c

Question - 6

Which of the following is a trinomial in p?

  • A x2+ 5
  • B p3+p2+\(\sqrt { 2 } \)
  • C \(\sqrt { p } (1+\sqrt { 2p } )\)
  • D \(y+\frac { 1 }{ y } +\frac { 1 }{ 2 } \)

Question - 7

Identify one of the factors of \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } +2-2x-\frac { 2 }{ x } \) from the following

  • A \(x-\frac { 1 }{ x } \)
  • B \(x+\frac { 1 }{ x } -1\)
  • C \(x+\frac { 1 }{ x } \)
  • D \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \)

Question - 8

If the factors of a2 + b2 + 2(ab + bc + ca) are (a + b + m) and (a + b + nc), find the value of m + n.

  • A 0
  • B 2
  • C 4
  • D 6

Question - 9

If (x2+ 3x + 5) (x2- 3x + 5) = m2 - n2,find m.

  • A x2-3x
  • B 3x+5
  • C x2+5
  • D x2-5

Question - 10

If \(\frac { x }{ y } +\frac { y }{ x } \)=-1(x, y \(\neq \) 0), what is the value of x3-y3?

  • A 1
  • B -1
  • C \(\frac { 1 }{ 2 } \)
  • D 0
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