Learn Polynomials for CAT Quantitative Aptitude

Polynomials

Expressions like the following are called polynomials in one variable.

0, -5, 7 etc. are examples of constant polynomials. The constant polynomial 0 is also the zero polynomial.

Others like 7x + 9 is a polynomial in variable x. Similarly, -6t³ is a polynomial in variable t. These are called polynomials in one variable.

A polynomial is an algebraic expression that is a sum of a number of terms. The name comes from the Greek words poly (many) and nomen (names or terms).

Example:

Notice the exponents on the terms. The first term has exponent 2; the second term has an understood exponent 1; and the last   term doesn't have any variable at all.

Polynomials are usually written this way, with the terms written in "decreasing" order; that is, with the highest exponent first, the next highest next, and so forth, until you get down to the plain old number.

The first term in the polynomial, when the terms are written in decreasing order, is also the term with the biggest exponent, and is called the “leading term”.

Coefficients of the Terms

When a term contains both a number and a variable part, the number part is called the “coefficient”. The coefficient on the leading term is called the leading coefficient.

In the above example, the coefficient of the leading term is 4; the coefficient of the second term  is 3; the constant term doesn’t have a coefficient.

Degree of the Polynomial

The exponent on a term tells you the “degree” of the term. For instance, the leading term in the above the above polynomial is a “second-degree term”. The second term is a “first degree” term.

The degree of the leading term tells you the degree of the polynomial.

is a polynomial of degree 6, since the expression could be written as:

Based on their degree:

• second-degree polynomial, such as 4x2, x2 – 9, or ax2 + bx + c, is also called a “quadratic”
• a third-degree polynomial, such as –6x3 or x3 – 27, is  also called a “cubic”
• a fourth-degree polynomial, such as x4 or 2x4 – 3x2 + 9, is sometimes called a “quartic”

Also note,

• The degree of a non-zero constant polynomial is zero.
• The degree of a zero constant polynomial is not defined.