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:
- The polynomial y^2 + 8y +1 has constant term equal to 1.
- The polynomial a^4 + 6a^2 +2a -7 has constant term equal to -7. Notice that the constant term (free from the variable “a”) is a negative number
- The polynomial \frac{3x}{5} + \frac{7}{9} has constant term equal to \frac{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 x^3-4x^2+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) = x^3-4x^2+8x+9 then p(0) = 0^3-4\times 0^2+8\times 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.
Constant term in quadratic equation
A quadratic polynomial is of the form ax^2+bx+c. Here the highest power of “x” is 2. The constant term in this case is “c”. Note that it can be both positive or negative.
- The quadratic polynomial 3x^2+4x+2 has constant term equal to 2.
- The quadratic polynomial x^2+7x-3 has constant term equal to -3. Notice that here the constant term is negative.
