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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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