Mathematics ยท Quantitative Aptitude

Algebraic Polynomials

138 Questions

Algebraic polynomials involve factoring expressions, applying the remainder theorem, and finding variable roots. These topics form a major part of the quantitative aptitude syllabus. Regular practice ensures accuracy in solving complex algebraic equations.

Factoring polynomialsFactor theoremRemainder theoremPolynomial rootsCubic polynomials

Algebraic Polynomials Questions

Multiple choice

What is the rational root theorem?

  1. Every rational root of a polynomial with integer coefficients is of the form \(p/q\), where \(p\) is a factor of the constant term and \(q\) is a factor of the leading coefficient.
  2. Every rational root of a polynomial with integer coefficients is of the form \(p/q\), where \(p\) is a factor of the leading coefficient and \(q\) is a factor of the constant term.
  3. Every rational root of a polynomial with integer coefficients is of the form \(p/q\), where \(p\) is a factor of the constant term and \(q\) is the leading coefficient.
  4. Every rational root of a polynomial with integer coefficients is of the form \(p/q\), where \(p\) is the leading coefficient and \(q\) is a factor of the constant term.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rational root theorem states that every rational root of a polynomial with integer coefficients is of the form (p/q), where (p) is a factor of the constant term and (q) is a factor of the leading coefficient.

Multiple choice

What is Descartes' rule of signs?

  1. The number of positive real roots of a polynomial is equal to the number of sign changes in the coefficients of the polynomial.

  2. The number of negative real roots of a polynomial is equal to the number of sign changes in the coefficients of the polynomial.

  3. The number of positive real roots of a polynomial is equal to the number of sign changes in the coefficients of the polynomial, plus the number of negative coefficients.

  4. The number of negative real roots of a polynomial is equal to the number of sign changes in the coefficients of the polynomial, plus the number of positive coefficients.
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A Correct answer
Explanation

Descartes' rule of signs states that the number of positive real roots of a polynomial is equal to the number of sign changes in the coefficients of the polynomial.

Multiple choice

Which mathematical concept is central to the study of polynomials?

  1. Variables

  2. Exponents

  3. Coefficients

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

The degree of a polynomial is a central concept in the study of polynomials, as it determines the highest power of the variable in the polynomial and influences its behavior.