Polynomials – MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025

Question 1:

\[
\text{If } P(x) = x^3 – 4x^2 + 3x + 5, \text{ what is } P(2)?
\]
\[
\text{(a) } 1, \quad \text{(b) } 3, \quad \text{(c) } 5, \quad \text{(d) } 7
\]
Answer: C

Question 2:

\[
\text{Which of the following is a polynomial?}
\]
\[
\text{(a) } x^2 + \frac{1}{x}, \quad \text{(b) } 3x^4 + 2x – 7, \quad \text{(c) } \sqrt{x} + 5, \quad \text{(d) } x^{-3} + x
\]
Answer: B

Question 3:

\[
\text{If } x-2 \text{ is a factor of } P(x) = x^3 – 5x^2 + ax + 10, \text{ find } a.
\]
\[
\text{(a) } 3, \quad \text{(b) } 5, \quad \text{(c) } 7, \quad \text{(d) } 9
\]
Answer: A

Question 4:

\[
\text{The degree of the polynomial } 7x^5 – 3x^3 + 2x^8 + 4 \text{ is:}
\]
\[
\text{(a) } 3, \quad \text{(b) } 5, \quad \text{(c) } 8, \quad \text{(d) } 4
\]
Answer: C

Question 5:

\[
\text{What is the remainder when } x^4 + 3x^3 – 2x + 7 \text{ is divided by } x – 1?
\]
\[
\text{(a) } 7, \quad \text{(b) } 9, \quad \text{(c) } 6, \quad \text{(d) } 5
\]
Answer: A

Question 6:

\[
\text{Which polynomial identity represents } (a+b)^3?
\]
\[
\text{(a) } a^3 + 3a^2b + 3ab^2 + b^3, \quad \text{(b) } a^3 – b^3,
\]
\[
\text{(c) } (a+b)(a-b), \quad \text{(d) } a^3 – 3a^2b + 3ab^2 – b^3
\]
Answer: A

Question 7:

\[
\text{Which of the following is a monomial?}
\]
\[
\text{(a) } x^2 + 2x, \quad \text{(b) } 4x^3, \quad \text{(c) } 3x^2 + 5x + 7, \quad \text{(d) } x – 1
\]
Answer: B

Question 8:

\[
\text{If } P(x) = x^3 + ax^2 + bx + 6 \text{ has roots } 1, 2, 3, \text{ find } a + b.
\]
\[
\text{(a) } -5, \quad \text{(b) } -6, \quad \text{(c) } -7, \quad \text{(d) } -8
\]
Answer: B

Question 9:

\[
\text{If } P(x) = x^3 – 2x + 5, \text{ then the coefficient of } x \text{ is:}
\]
\[
\text{(a) } -2, \quad \text{(b) } 3, \quad \text{(c) } 5, \quad \text{(d) } 1
\]
Answer: A

Question 10:

\[
\text{If } P(x) = x^4 – 3x^3 + 2x^2 – 4x + 7, \text{ then the leading coefficient is:}
\]
\[
\text{(a) } -3, \quad \text{(b) } 2, \quad \text{(c) } 1, \quad \text{(d) } 4
\]
Answer: C

Question 11:

\[
\text{The sum of the roots of the polynomial } x^3 – 7x^2 + 10x – 5 = 0 \text{ is:}
\]
\[
\text{(a) } 7, \quad \text{(b) } 5, \quad \text{(c) } -7, \quad \text{(d) } -5
\]
Answer: A

Question 12:

\[
\text{Which of the following represents the zero polynomial?}
\]
\[
\text{(a) } x^2 + x, \quad \text{(b) } 0, \quad \text{(c) } x^3 – x, \quad \text{(d) } x^2 – 1
\]
Answer: B

Question 13:

\[
\text{The degree of a non-zero constant polynomial is:}
\]
\[
\text{(a) } 1, \quad \text{(b) } 0, \quad \text{(c) } -1, \quad \text{(d) } None
\]
Answer: B

Question 14:

\[
\text{If } P(x) = x^3 – 3x^2 + 4x – 2, \text{ find } P(1).
\]
\[
\text{(a) } 0, \quad \text{(b) } 3, \quad \text{(c) } 1, \quad \text{(d) } 2
\]
Answer: D

Question 15:

\[
\text{Which of the following polynomials is a quadratic polynomial?}
\]
\[
\text{(a) } x^3 + x^2, \quad \text{(b) } x^2 – 4x + 5, \quad \text{(c) } x + 7, \quad \text{(d) } x^4 + 3x^2
\]
Answer: B

More MCQs on Algebra (Collected from Past Papers)

  1. Elementary Algebra – MCQs
  2. Algebraic Expressions – MCQs
  3. Algebraic Identities – MCQs
  4. Commutative Algebra – MCQs
  5. Linear Equations – MCQs
  6. Graphing Linear Equations – MCQs
  7. Inequalities in Algebra – MCQs
  8. Absolute Value Inequalities – MCQs
  9. Exponent – MCQs
  10. Exponential Functions – MCQs
  11. Logarithms – MCQs
  12. Polynomials – MCQs
  13. Factoring Methods – MCQs
  14. Polynomial Arithmetic – MCQs
  15. Quadratic Equation – MCQs
  16. Linear Algebra – MCQs
  17. Matrices in Algebra – MCQs
  18. Functions in Algebra – MCQs
  19. Sequences in Algebra – MCQs
  20. Arithmetic in Algebra – MCQs
  21. Combining Like Terms in Algebra – MCQs
  22. Abstract Algebra – MCQs
  23. Sets in Algebra – MCQs
  24. Algebra Calculator – MCQs

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