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 maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

The algebraic expression for the statement "Product of $x$ and reciprocal of $a$, subtracted from the product of $y$ and reciprocal of $b"$ is ___________.

  1. $\dfrac {y}{b} - \dfrac {x}{a}$
  2. $\dfrac {y - x}{a - b}$
  3. $xa - yb$
  4. $\dfrac {1}{yb - xa}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Product of $x$ and reciprocal of $a$ $=$ $x\times \dfrac{1}{a}= \dfrac{x}{a}$
Product of $y$ and reciprocal of $b$ $=$ $y\times \dfrac{1}{b}= \dfrac{y}{b}$
Therefore, the algebraic expression is $\dfrac{y}{b}-\dfrac{x}{a}$.

Hence, option A is correct.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

The algebraic expression for the statement 'thrice of $x$ is added to $y$ multiplied by itself' is __________.

  1. $3x + 2y$
  2. $3x + y^{2}$
  3. $3(x + y^{2})$
  4. $3x + y$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Thrice of $x$ $=$ $3x$


$y$ multiplied by itself $=$ $y\times y=y²$
 
According to question, we have

The algebraic expression is $3x+ y²$.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Get the algebraic expression in the following cases using variables, constant and arithmetic operations.
Subtraction of $z$ from $y$.

  1. $y+z$
  2. $y-z$
  3. $z-y$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Subtraction of $z$ from $y$ implies that a number of value $z$ is to be subtracted from another number of $y$ value $y$ which means $y-z$.

Multiple choice

Expand ( a - b )2

  1. a2 - b2

  2. -ab2

  3. a2 - 2ab + b2

  4. a2 + b2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The expansion of (a - b)^2 is a^2 - 2ab + b^2 based on the binomial square identity.

Multiple choice

(-5)+8 =

  1. -3

  2. +3

  3. 5

  4. -5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

-5 + 8 is equivalent to 8 - 5, which equals 3.

Multiple choice

The factors of 15pq + 15 + 9q + 25p is

  1. ( 5p + 3)( 3q + 5)

  2. ( 5p +3)(q +5)

  3. ( p + 3)( 3q + 5)

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

Factor by grouping: 15pq + 25p + 9q + 15 = 5p(3q + 5) + 3(3q + 5). Factoring out the common binomial (3q + 5) yields (5p + 3)(3q + 5).

Multiple choice

Factors of x2 -7x +12 is

  1. (x +3)(x +4)

  2. (x +3)(x -4)

  3. (x-3)(x -4)

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To factor x^2 - 7x + 12, find two numbers that multiply to 12 and add to -7. These numbers are -3 and -4, so the factors are (x - 3)(x - 4).