Coefficient Of Polynomial

 

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 9; the coefficient of the second term is 6; the constant term doesn't have a coefficient.

As we know "poly" in "polynomial" means "many", the term "polynomial" should only refer to sums of many terms, but the term is used to refer to anything from one term to the sum of a zillion terms. However, the shorter polynomials do have their own names:

 

one-term polynomial

3x or 4x²,

Monomial - "mono" meaning "one"

two-term polynomial

3x + y or x² – 7

Binomial - "bi" meaning "two"

three-term polynomial

2x + y + z or x4 + 4x2 – 4

Trinomial - "tri" meaning "three"

"Evaluating" a polynomial is the same as evaluating anything else: you replace in the given value of x, and find out what y is supposed to be.

For Example:

Evaluate 2x3 – x2 – 4x + 2 at x = – 5

Put "–5" for the "x", remembering to be careful with my parentheses and the negatives:

2(–5)3 – (–5)2 – 4(–5) + 2 
=  2(–125) – (25) + 20 + 2 
=  –250 – 25 + 22 
=  –63 -3 
=  –66