Classes IX & X Mathematics

Chapter 2: Polynomials

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Worksheet Details:

  • Title: Class IX Math: Polynomials Printable Sheet
  • Format: Print Optimized CSS stylesheet
  • Sections: Formulas checklist, 5 assessment questions, worked keys

NexPro Education Worksheet

Class IX Mathematics: Polynomials

Name: ______________________Date: __________________Score: ______ / 5

Section I: Key Formulas

Factor Theorem
P(c) = 0 \Rightarrow (x-c) \text{ is a factor}
Cubic Expansion Identity
(a+b)^3 = a^3 + b^3 + 3ab(a+b)

Section II: Answer the Questions

1. If 2x + 3y = 12 and xy = 6, find the value of 8x3 + 27y3.

Solve and write the step-by-step solution in the workspace below.

2. Find the value of a and b so that x + 1 and x - 1 are factors of x4 + ax3 + 2x2 - 3x + b.

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3. Find the value of m and n so that the polynomial f(x) = x3 - 6x2 + mx - n is exactly divisible by (x -1) as well as (x - 2).

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4. Find the value of k, if x + k is factor of the polynomials: (i) x3 - (k2 - 1)x + 3 (ii) - 4x3 + 4x2 + 4kx - k

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5. Find the value of a and b so that polynomial p(x) = x3 - 3x2 - ax + b has (x + 1) and (x - 5) as factors.

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