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Discover the Path to Mathematical Mastery
An Education That Counts
A polynomial is a linear expression of terms consisting of coefficients and variables whose powers are nonnegative integers. Polynomials may be single variate such as \(2x^3+3x+6\), or they may be multivariate such as \(x^2y^2+2xy^2-3x+5\).
The degree of a polynomial is the maximum sum of the exponents for each term in the polynomial. For instance, the degree of \(f(x,y)=x^2y^2+3x^2y+x^2\) is \(deg(fx,y)=4\) since \(2+2=4\) is greater than \(2+1=3\) and \(2\). The degree of a single variate polynomial corresponds to the highest power within the given polynomial.
The vertex form for the quadratic \(f(x)=ax^2+bx+c\) is of the form \(f(x)=a(x-h)^2+k\).
The vertex is the point \((h,k)\) on the quadratic.
The value \(y=k\) is maximum on the quadratic provided that \(a<0\), and \(y=k\) is a minimum if \(a>0\). The process of finding the x-coordinate of the vertex can be found completing the square. This value can also be found by noting that \(\displaystyle x=\frac{-b}{2a}\).
| Number of Terms | Classification |
| One Term | Monomial |
| Two Terms | Binomial |
| Three Terms | Trinomial |
| Four Terms | Quadnomial |
| Highest Degree | Classification |
| Degree One | Linear |
| Degree Two | Quadratic |
| Degree Three | Cubic |
| Degree Four | Quartic |
| Degree Five | Quintic |
Binomial Theorem
Roots
Definition Roots
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| S | M | T | W | T | F | S |
|---|---|---|---|---|---|---|
| 1 | 2 | |||||
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| 24 | 25 | 26 | 27 | 28 | 29 | 30 |
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