Polynomial comes from poly – means “many” and -nomial (means “term”). So, it is many terms.
An expression of form p(x) = a0+a1x+a2x2…..+anxn, where an ≠ 0, is called polynomial in x of degree n.
So, polynomials can include:
Let us consider a few examples and check whether they are polynomials are or not?
Polynomials have special names like monomial, binomial, trinomial which have 1, 2 and 3 terms respectively.
5b3c, 2a, a2 are monomials.
2a+7b, 3x+5, 9y - 2y2 are binomials.
-3x2+2+3x, 9y - 2y2-y are trinomials.
A polynomial can have no variable, one variable or two or more variables.
The degree of the polynomial is the highest exponent of the variable. Polynomials with degree 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
x2 - 5x - 4
The standard form of writing a polynomial is writing in decreasing order of terms. The largest term or the term with highest exponent is written first and is called the leading term in the polynomial.
For example, x5 + 2x3 + 4x2 – 10.
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