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
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$a *= pow (2, 2);
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$a >>= 2;
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$a <<= 2;
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$a = $a $a;
A,C
Correct answer
Explanation
In PHP, '$a <<= 2' shifts the bits of $a two places to the left, which is equivalent to multiplying by 2 squared (4). The first option '$a *= pow(2, 2)' also results in $a * 4. Since this is a multiple-choice question with two correct options, both are valid logic.
C
Correct answer
Explanation
In a full factorial design, the total number of trials equals the product of all factor levels. Here: X1 (3 levels) × X2 (3 levels) × X3 (4 levels) = 3 × 3 × 4 = 36 trials. This ensures every possible combination of factor levels is tested. The other options (10, 16, 13) don't match this calculation.
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5x + 14y
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5x + 16y
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5x + 5y
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6x + 4y
A
Correct answer
Explanation
Step 1: 2x + 5y. Step 2: 3(2x + 5y) = 6x + 15y. Step 3: (6x + 15y) - (x + y) = 5x + 14y. The calculation follows basic algebraic distribution and subtraction of like terms.
C
Correct answer
Explanation
By comparing the two expressions, we see they are identical except for the terms -(c/x) in (i) and -(c/a) in (ii). For the expressions to be equal, the denominators must be the same, meaning x must equal a.
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a^6+5a^6b+20a^3b^2+10a^2b^3+15a^5b^4+8ab^5+b^6+0a^1+0b^6
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a^6-5a^6b+20a^3b^2-10a^2b^3+15a^5b^4-8ab^5+b^6
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a^6+5a^5b+10a^4b^3+10a^3b^4+5ab^5+b^6
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a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6
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.
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n*x -(a+b+..z)
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0
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x^n-abc..
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none
B
Correct answer
Explanation
The series includes the term (x-x), which is 0. Since any number multiplied by 0 is 0, the entire product of the series is 0.
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6x^3y^4z^3
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24xy^2z^2
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18x^2y^2z^3
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6xy^2z^2
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6x^3y^4z^4
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.
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.
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(6x - 1)(x + 2)
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(3x - 1)(2x + 2)
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(3x + 1)(2x - 2)
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(6x + 1)(x - 2)
D
Correct answer
Explanation
To factor $6x^2 - 11x - 2$, we look for factors of $6 \times -2 = -12$ that sum to $-11$. These are $-12$ and $1$. Thus, $6x^2 - 12x + x - 2 = 6x(x - 2) + 1(x - 2) = (6x + 1)(x - 2)$. This matches option 129049.
D
Correct answer
Explanation
The numbers are -8, (2 - [-8]) = 10, 3, 7, and -1. The sum is -8 + 10 + 3 + 7 - 1 = 11. The mean is 11 divided by 5, which equals 2.2.
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3x^2 + x - 14
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3x^2 - 13x - 14
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3x^2 - x - 14
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3x^2 - 14
C
Correct answer
Explanation
Using the FOIL method: (x+2)(3x-7) = x(3x) + x(-7) + 2(3x) + 2(-7) = 3x² - 7x + 6x - 14 = 3x² - x - 14. Option A has the wrong middle term (+x instead of -x), Option B has -13x instead of -x, and Option D is missing the x term entirely.
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Perfect Number
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Rational Number
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None of the options
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Sublime Number
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).
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Perfect Number
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Rational Number
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None of the options
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Sublime Number
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).
B
Correct answer
Explanation
FOIL stands for First, Outer, Inner, Last - the systematic method for multiplying two binomials. Example: (x+2)(x+3) = x² + 3x + 2x + 6 = x² + 5x + 6. FIOL, FLIO, and FUEL are incorrect acronyms.
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.