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

-2x1+2=?

  1. 4

  2. 6

  3. 0

  4. -6

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

-2x1+2=-2+2=0

Multiple choice

Add 7x2 + 8x + 3 and 8x + 3x2 + 9.

  1. 8x2 + 16x + 12

  2. 10x2 + 8x + 12

  3. 10x2 + 16x + 12

  4. 10x2 + 16x + 6

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

7x2 + 8x + 3 + 8x + 3x2 + 9 = 8x + 3x2 + 9 + 7x2 + 8x + 3 = 10x2 + 16x + 12

Multiple choice

Which of the following expressions is a linear expression?

  1. – 4x – 7xy2

  2. 4x – 3y
  3. $\frac{4}{3}$ + $\frac{1}{x} + x$

  4. x2 + 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The highest power of the term in the given expression is called degree. The expression having degree one is a linear expression. So, 4x – 3y is a linear expression.

Multiple choice

Which of the following expressions is a linear expression?

  1. 4x + 3y + 2

  2. 3xy + 2y + 2

  3. xy + 2y + 3y

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

The highest power of the term in the given expression is called degree. An expression having degree one is a linear expression. Therefore, 4x + 3y + 2 is the linear expression.

Multiple choice maths algebraic formulae - expansion of squares introduction to factorization introduction to factorisation factorising algebraic expressions

Factorise ${\left( {3 - 4y - 7{y^2}} \right)^2} - {\left( {4y + 1} \right)^2}$ 

  1. $\left( {4 - 7{y^2}} \right)\left( {2 - 8y - 7{y^2}} \right)$
  2. $\left( {7{y^2} - 4} \right)\left( {2 - 8y - 7{y^2}} \right)$
  3. $\left( {4 - 7{y^2}} \right)\left( {7{y^2} + 8y - 2} \right)$
  4. $\left( {7{y^2} - 4} \right)\left( {7{y^2} - 8y - 2} \right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We have,

${\left( {3 - 4y - 7{y^2}} \right)^2} - {\left( {4y + 1} \right)^2}$ 

We know that
$a^2-b^2=(a+b)(a-b)$

Therefore,
$\Rightarrow (3 - 4y - 7y^2+4y + 1)(3-4y-7y^2-4y-1) $ 

$\Rightarrow (4 - 7y^2)(2-8y-7y^2) $ 

Hence, this is the answer.