Mathematics · 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

What are the real factors of the expression (x2 + 4)?

  1. (x2 + 2) and (x2 + 2)

  2. (x2 + 2) and (x2 - 2)

  3. x2 and (x2 + 4)

  4. (x2 + 2x + 2) and (x2 - 2x + 2)

  5. Non existent
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

It is understood that we restrict ourselves to rational coefficients and integral powers of 'x'. With this restriction, (x2 + 4) is not factorisable. Hence, option (5) is the correct answer.

Multiple choice

Which of the following algebraic equations is not the same as the equation 210x2 + 21xy + 2z3 + 2xyz?

  1. (2x) (15x) (7) + (3xy) (7xy) + 2z3 + 2 (xyz) (xyz)

  2. (2x) (15x) (7) + 3xy + 18xy + 2z2 z + xyz + xyz

  3. (2x) (15x) (7) + 3xy + 18xy + 2z3 + xyz + xyz

  4. (2x) (15) (7x) + 3xy + 18xy + 2z2 z + xyz + xyz

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

It is equal to 210 x2 + 21x2 y2 + 2 x2y2z2. It is not equal to the given equation 210 x2 + 21 xy + 2z3 + 2xyz. Hence, this option is the correct answer.