Mathematics ยท Quantitative Aptitude

Algebraic Expressions and Polynomials

292 Questions

Algebraic expressions and polynomials form the foundation of algebra, involving variables, constants, and mathematical operations. This topic is heavily tested in the quantitative aptitude sections of SSC, banking, and state exams. Use these questions to practice expanding, factoring, and simplifying various polynomial expressions.

Expanding algebraic expressionsFactoring polynomialsAlgebraic identitiesFinding common factorsSimplifying numerical statements

Algebraic Expressions and Polynomials Questions

Multiple choice

Divide (x^4 - 2x^3 + 3x^2 - 4x + 5) by (x - 1).

  1. \(x^3 - x^2 + 2x - 3\)
  2. \(x^3 - x^2 + 2x + 3\)
  3. \(x^3 + x^2 + 2x + 3\)
  4. \(x^3 + x^2 + 2x - 3\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using polynomial long division, we find that the quotient is (x^3 - x^2 + 2x - 3) with a remainder of 2.

Multiple choice

Divide (x^3 - 3x^2 + 2x - 5) by (x - 1).

  1. \(x^2 - 2x + 3\)
  2. \(x^2 - 2x - 3\)
  3. \(x^2 + 2x + 3\)
  4. \(x^2 + 2x - 3\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using polynomial long division, we find that the quotient is (x^2 - 2x + 3) with a remainder of 2.

Multiple choice

What is the result of dividing (6x^2 - 11x + 3) by (3x - 1)?

  1. \(2x - 3\)
  2. \(2x + 3\)
  3. \(2x - 1\)
  4. \(2x + 1\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using synthetic division, we find that the quotient is (2x - 3) with a remainder of 6.

Multiple choice

Divide (x^4 - 2x^3 + 3x^2 - 4x + 5) by (x - 1).

  1. \(x^3 - x^2 + 2x - 3\)
  2. \(x^3 - x^2 + 2x + 3\)
  3. \(x^3 + x^2 + 2x + 3\)
  4. \(x^3 + x^2 + 2x - 3\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using polynomial long division, we find that the quotient is (x^3 - x^2 + 2x - 3) with a remainder of 2.

Multiple choice

Evaluate the expression: ( 2^3 \cdot 2^5 )

  1. \( 2^6 \)
  2. \( 2^8 \)
  3. \( 2^{10} \)
  4. \( 2^{15} \)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the rule of exponents, ( a^m \cdot a^n = a^(m+n) ), we have ( 2^3 \cdot 2^5 = 2^(3+5) = 2^8 ).

Multiple choice

Evaluate the expression: ( 5^0 )

  1. \( 0 \)
  2. \( 1 \)
  3. \( 5 \)
  4. \( 25 \)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Any number raised to the power of 0 is equal to 1. Therefore, ( 5^0 = 1 ).

Multiple choice

Factorize the polynomial x^3 - 2x^2 - 5x + 6.

  1. (x - 1)(x - 2)(x + 3)

  2. (x + 1)(x - 2)(x - 3)

  3. (x - 1)(x + 2)(x - 3)

  4. (x + 1)(x + 2)(x - 3)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We can factorize the polynomial using synthetic division or by grouping terms. By grouping, we have: (x^3 - 2x^2) - (5x - 6) = x^2(x - 2) - 1(x - 2) = (x^2 - 1)(x - 2) = (x - 1)(x + 1)(x - 2).