What is the Constant Term of a Polynomial?

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The constant term of a polynomial refers to the term in the polynomial in which the variable/letter does not appear. For example, given the polynomial “3x + 4” the constant term is 4 since “x” does not appear alongside 4.

Examples:

1. The polynomial y2 + 8y +1 has a constant term equal to 1.
2. The polynomial a4 + 6a2 +2a -7 has a constant term equal to -7. Notice that the constant term (free from the variable “a”) is a negative number
3. The polynomial 3x/5 + 7/9 has a constant term equal to 7/9.

How to find the constant term of a polynomial?

In order to find the constant term of a polynomial, we should simply look at the term where the variable/letter is absent.

For instance, in the polynomial x3-4x2+8x+9, we see that 9 is free of the letter “x”. So for this polynomial, the constant term is equal to +9.

Given a polynomial p(x) another way to find the constant term is to simply put x=0, that is finding p(0).

So if p(x) = x3-4x2+8x+9 then p(0) = 03-4*02+8*0+9 = 9. Hence we conclude that the constant term of the polynomial is 9.

If a polynomial is given in the standard form (in descending order of degree) then the term occurring at the last is the constant term.

A quadratic polynomial is of the form ax2+bx+c. Here the highest power of “x” is 2. The constant term, in this case, is “c”. Note that it can be both either positive or negative.

1. The quadratic polynomial 3x2+4x+2 has a constant term equal to 2.
2. The quadratic polynomial x2+7x-3 has a constant term equal to -3. Notice that here the constant term is negative.
Summary
Article Name
What is the Constant Term of a Polynomial?
Description
The constant term of a polynomial refers to the term in the polynomial in which the variable/letter does not appear. For example, given the polynomial "3x + 4" the constant term is 4 since "x" does not appear alongside 4.
Publisher Name
allthingsstatistics.com