Mathematics · Quantitative Aptitude

Algebraic Expressions and Polynomials

275 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 general knowledge math & puzzles

The expantion of (a+b)^6 is ________ (^ is Power)

  1. a^6+5a^6b+20a^3b^2+10a^2b^3+15a^5b^4+8ab^5+b^6+0a^1+0b^6

  2. a^6-5a^6b+20a^3b^2-10a^2b^3+15a^5b^4-8ab^5+b^6

  3. a^6+5a^5b+10a^4b^3+10a^3b^4+5ab^5+b^6

  4. a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

According to the Binomial Theorem, the coefficients for (a+b)^6 follow the 6th row of Pascal's Triangle: 1, 6, 15, 20, 15, 6, 1. Option 39352 correctly applies these coefficients and decreasing/increasing powers for a and b respectively.

Multiple choice general knowledge math & puzzles

Find the G.C.D of 12x^2y^3z^2, 18x^3y^2z^4, and 24xy^4z^3

  1. 6x^3y^4z^3

  2. 24xy^2z^2

  3. 18x^2y^2z^3

  4. 6xy^2z^2

  5. 6x^3y^4z^4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find GCD, take the lowest power of each common variable: for coefficient, GCD of 12, 18, 24 is 6. For x: lowest power is x (x^1 from third term). For y: lowest power is y^2 (from second term). For z: lowest power is z^2 (from first term). So GCD = 6xy^2z^2, which is option D.

Multiple choice general knowledge math & puzzles

find the value of the expression 1-6+2-7+3-8... 100 terms

  1. -500

  2. -250

  3. -600

  4. -200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The series consists of 100 terms which can be grouped into 50 pairs: (1-6), (2-7), (3-8), and so on. Each pair simplifies to -5. Multiplying the value of one pair (-5) by the total number of pairs (50) results in -250. Other options are incorrect because they miscalculate the number of pairs or the value per pair.

Multiple choice general knowledge math & puzzles

The number 12 has 6 factors: 1, 2, 3, 4, 6, and 12. If you add up those factors you will get 28. Because of this fact, and the special properties of 6 and 28, the number 12 is called a _______ number.

  1. Perfect Number

  2. Rational Number

  3. None of the options

  4. Sublime Number
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A sublime number is a number where the total count of its divisors is a perfect number and the sum of its divisors is also a perfect number. 12 has 6 divisors (perfect) and they sum to 28 (perfect).

Multiple choice general knowledge math & puzzles

The number 12 has 6 factors: 1, 2, 3, 4, 6, and 12. If you add up those factors you will get 28. Because of this fact, and the special properties of 6 and 28, the number 12 is called a _______ number.

  1. Perfect Number

  2. Rational Number

  3. None of the options

  4. Sublime Number
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A sublime number is a positive integer which has a perfect number of positive divisors, and the sum of its divisors is also a perfect number. 12 has 6 divisors (6 is perfect) and their sum is 28 (28 is perfect).

Multiple choice general knowledge math & puzzles

2 X 2 + 2

  1. 8

  2. 6

  3. 4

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Following order of operations (PEMDAS/BODMAS), multiplication comes before addition. First calculate 2 X 2 = 4, then add 2 to get 6.

Multiple choice general knowledge math & puzzles

2*(2+(2/2*(2+2)*2-2))

  1. 16

  2. 0

  3. 8

  4. 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Working through the inner parentheses first: 2+2=4, then 2/2=1, so 1*4*2=8, then 8-2=6, then 2+6=8, then 2*8=16, which is option A. This requires careful application of order operations - work from innermost parentheses outward. Option C (8) is a common error if you stop halfway through the calculation.

Multiple choice general knowledge math & puzzles

2*3*5-(10*3)-3+4

  1. 0

  2. -1

  3. 1

  4. Nahi Chalega
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using order of operations (PEMDAS/BODMAS): First calculate multiplications from left to right: 2×3×5 = 30, and 10×3 = 30. Then perform subtraction and addition: 30 - 30 - 3 + 4 = 1.