Mathematics ยท 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 is the product of (x^2 - 2x + 1) and (x + 3)?

  1. x^3 + x^2 - 5x + 3

  2. x^3 + x^2 - 5x - 3

  3. x^3 - x^2 - 5x + 3

  4. x^3 - x^2 - 5x - 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x^2 - 2x + 1) and (x + 3), we use the distributive property. First, we multiply x^2 by x and x^2 by 3, which gives us x^3 and 3x^2. Then, we multiply -2x by x and -2x by 3, which gives us -2x^2 and -6x. Finally, we multiply 1 by x and 1 by 3, which gives us x and 3. We then add the like terms to get x^3 + x^2 - 5x + 3.

Multiple choice

What is the product of (3x^2y - 2xy + 4) and (2x - 3y)?

  1. 6x^3y^2 - 10x^2y^2 + 11xy - 12y

  2. 6x^3y^2 - 10x^2y^2 + 11xy + 12y

  3. 6x^3y^2 + 10x^2y^2 + 11xy - 12y

  4. 6x^3y^2 + 10x^2y^2 + 11xy + 12y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (3x^2y - 2xy + 4) and (2x - 3y), we use the distributive property. First, we multiply 3x^2y by 2x and 3x^2y by -3y, which gives us 6x^3y^2 and -9x^2y^2. Then, we multiply -2xy by 2x and -2xy by -3y, which gives us -4x^2y and 6xy. Finally, we multiply 4 by 2x and 4 by -3y, which gives us 8x and -12y. We then add the like terms to get 6x^3y^2 - 10x^2y^2 + 11xy - 12y.

Multiple choice

What is the product of (x + 2)(x - 2)(x^2 + 4)?

  1. x^4 - 16

  2. x^4 + 16

  3. x^4 - 8

  4. x^4 + 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x + 2)(x - 2)(x^2 + 4), we first multiply (x + 2) and (x - 2) using the difference of squares formula. This gives us x^2 - 4. Then, we multiply x^2 - 4 by x^2 + 4 using the sum of cubes formula. This gives us x^4 - 16.

Multiple choice

What is the product of (x^3 - 2x^2 + x - 2)(x^2 + 3x - 4)?

  1. x^5 + x^4 - 7x^3 - 14x^2 + 11x + 8

  2. x^5 + x^4 - 7x^3 - 14x^2 + 11x - 8

  3. x^5 - x^4 - 7x^3 + 14x^2 + 11x + 8

  4. x^5 - x^4 - 7x^3 + 14x^2 + 11x - 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x^3 - 2x^2 + x - 2)(x^2 + 3x - 4), we use the distributive property. First, we multiply x^3 by x^2, x^3 by 3x, x^3 by -4, -2x^2 by x^2, -2x^2 by 3x, -2x^2 by -4, x by x^2, x by 3x, x by -4, -2 by x^2, -2 by 3x, and -2 by -4. This gives us x^5, 3x^4, -4x^3, -2x^4, -6x^3, 8x^2, x^2, 3x, -4, -2x^2, -6x, and 8. We then add the like terms to get x^5 + x^4 - 7x^3 - 14x^2 + 11x + 8.

Multiple choice

What is the product of (2x + 3y)(3x - 2y)?

  1. 6x^2 - 9xy - 6y^2

  2. 6x^2 + 9xy - 6y^2

  3. 6x^2 - 9xy + 6y^2

  4. 6x^2 + 9xy + 6y^2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To multiply (2x + 3y)(3x - 2y), we use the distributive property. First, we multiply 2x by 3x and 2x by -2y, which gives us 6x^2 and -4xy. Then, we multiply 3y by 3x and 3y by -2y, which gives us 9xy and -6y^2. We then add the like terms to get 6x^2 - 9xy + 6y^2.

Multiple choice

What is the product of (x^2 + 2x + 1)(x - 1)?

  1. x^3 + x^2 - 1

  2. x^3 + x^2 + 1

  3. x^3 - x^2 - 1

  4. x^3 - x^2 + 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x^2 + 2x + 1)(x - 1), we use the distributive property. First, we multiply x^2 by x and x^2 by -1, which gives us x^3 and -x^2. Then, we multiply 2x by x and 2x by -1, which gives us 2x^2 and -2x. Finally, we multiply 1 by x and 1 by -1, which gives us x and -1. We then add the like terms to get x^3 + x^2 - 1.

Multiple choice

What is the product of (x^3 - 2x^2 + x - 2)(x + 1)?

  1. x^4 - x^3 - x^2 + x - 2

  2. x^4 - x^3 - x^2 - x - 2

  3. x^4 + x^3 - x^2 + x - 2

  4. x^4 + x^3 - x^2 - x - 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x^3 - 2x^2 + x - 2)(x + 1), we use the distributive property. First, we multiply x^3 by x and x^3 by 1, which gives us x^4 and x^3. Then, we multiply -2x^2 by x and -2x^2 by 1, which gives us -2x^3 and -2x^2. Next, we multiply x by x and x by 1, which gives us x^2 and x. Finally, we multiply -2 by x and -2 by 1, which gives us -2x and -2. We then add the like terms to get x^4 - x^3 - x^2 + x - 2.

Multiple choice

What is the product of (2x^2 - 3x + 4)(3x^2 + 2x - 1)?

  1. 6x^4 - 5x^3 - 11x^2 + 11x - 4

  2. 6x^4 - 5x^3 - 11x^2 - 11x - 4

  3. 6x^4 + 5x^3 - 11x^2 + 11x - 4

  4. 6x^4 + 5x^3 - 11x^2 - 11x - 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (2x^2 - 3x + 4)(3x^2 + 2x - 1), we use the distributive property. First, we multiply 2x^2 by 3x^2, 2x^2 by 2x, 2x^2 by -1, -3x by 3x^2, -3x by 2x, -3x by -1, 4 by 3x^2, 4 by 2x, and 4 by -1. This gives us 6x^4, 4x^3, -2x^2, -9x^3, -6x^2, 3x, 12x^2, 8x, and -4. We then add the like terms to get 6x^4 - 5x^3 - 11x^2 + 11x - 4.

Multiple choice

What is the product of (x^2 - 2x + 3)(x^2 + 2x - 3)?

  1. x^4 - 9

  2. x^4 + 9

  3. x^4 - 1

  4. x^4 + 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x^2 - 2x + 3)(x^2 + 2x - 3), we use the difference of squares formula. This gives us (x^2 - 2x + 3)(x^2 + 2x - 3) = (x^2)^2 - (2x - 3)^2 = x^4 - (4x^2 - 12x + 9) = x^4 - 4x^2 + 12x - 9.

Multiple choice

What is the product of (x^3 + 2x^2 - 3x + 4)(x^3 - 2x^2 + 3x - 4)?

  1. x^6 - 16

  2. x^6 + 16

  3. x^6 - 8

  4. x^6 + 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x^3 + 2x^2 - 3x + 4)(x^3 - 2x^2 + 3x - 4), we use the difference of squares formula. This gives us (x^3 + 2x^2 - 3x + 4)(x^3 - 2x^2 + 3x - 4) = (x^3)^2 - (2x^2 - 3x + 4)^2 = x^6 - (4x^4 - 12x^3 + 25x^2 - 24x + 16) = x^6 - 4x^4 + 12x^3 - 25x^2 + 24x - 16.

Multiple choice

What is the product of (2x^2 + 3x - 4)(2x^2 - 3x + 4)?

  1. 4x^4 - 9

  2. 4x^4 + 9

  3. 4x^4 - 1

  4. 4x^4 + 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (2x^2 + 3x - 4)(2x^2 - 3x + 4), we use the difference of squares formula. This gives us (2x^2 + 3x - 4)(2x^2 - 3x + 4) = (2x^2)^2 - (3x - 4)^2 = 4x^4 - (9x^2 - 24x + 16) = 4x^4 - 9x^2 + 24x - 16.

Multiple choice

What is the product of (x^4 + 2x^3 - 3x^2 + 4x - 5)(x^4 - 2x^3 + 3x^2 - 4x + 5)?

  1. x^8 - 16

  2. x^8 + 16

  3. x^8 - 8

  4. x^8 + 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x^4 + 2x^3 - 3x^2 + 4x - 5)(x^4 - 2x^3 + 3x^2 - 4x + 5), we use the difference of squares formula. This gives us (x^4 + 2x^3 - 3x^2 + 4x - 5)(x^4 - 2x^3 + 3x^2 - 4x + 5) = (x^4)^2 - (2x^3 - 3x^2 + 4x - 5)^2 = x^8 - (4x^6 - 12x^5 + 25x^4 - 40x^3 + 60x^2 - 40x + 25) = x^8 - 4x^6 + 12x^5 - 25x^4 + 40x^3 - 60x^2 + 40x - 25.

Multiple choice

What is the product of (x^5 + 2x^4 - 3x^3 + 4x^2 - 5x + 6)(x^5 - 2x^4 + 3x^3 - 4x^2 + 5x - 6)?

  1. x^10 - 16

  2. x^10 + 16

  3. x^10 - 8

  4. x^10 + 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To multiply (x^5 + 2x^4 - 3x^3 + 4x^2 - 5x + 6)(x^5 - 2x^4 + 3x^3 - 4x^2 + 5x - 6), we use the difference of squares formula. This gives us (x^5 + 2x^4 - 3x^3 + 4x^2 - 5x + 6)(x^5 - 2x^4 + 3x^3 - 4x^2 + 5x - 6) = (x^5)^2 - (2x^4 - 3x^3 + 4x^2 - 5x + 6)^2 = x^10 - (4x^8 - 12x^7 + 25x^6 - 40x^5 + 60x^4 - 40x^3 + 25x^2 - 60x + 36) = x^10 - 4x^8 + 12x^7 - 25x^6 + 40x^5 - 60x^4 + 40x^3 - 25x^2 + 60x - 36.

Multiple choice

What is the value of the expression (2 + 3i)(4 - 5i)?

  1. 22 - 11i

  2. 22 + 11i

  3. 14 - 22i

  4. 14 + 22i
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the distributive property, we can expand the expression as follows: (2 + 3i)(4 - 5i) = 2(4 - 5i) + 3i(4 - 5i) = 8 - 10i + 12i - 15i^2 = 8 + 2i - 15(-1) = 22 + 11i.

Multiple choice

What is Bhaskara II's method for solving quadratic equations?

  1. Completing the square

  2. Factoring

  3. Using the quadratic formula
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bhaskara II's method for solving quadratic equations is completing the square.