* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download One and Two digit Addition and Subtraction - Perfect Math
Survey
Document related concepts
Polynomial greatest common divisor wikipedia , lookup
Quartic function wikipedia , lookup
System of linear equations wikipedia , lookup
Horner's method wikipedia , lookup
Elementary algebra wikipedia , lookup
Factorization of polynomials over finite fields wikipedia , lookup
Fundamental theorem of algebra wikipedia , lookup
Canonical normal form wikipedia , lookup
Eisenstein's criterion wikipedia , lookup
Polynomial ring wikipedia , lookup
Transcript
Polynomial Basics Peter Gibby Polynomial • A polynomial has multiple variables that we cannot add together, such as x and y, or x and x2 • We can actually have as many variables and exponents of variables as we can fit. • There are ways to add, subtract, multiply, and divide these still even if the variables do not add up. Examples • • • • 4x+2y 2x2-x-y+y2 a+2b+3c+4d+5e+6f x6+4zx5+3yx11-9xz+5x2+x6y2z+xy6 Addition • Adding or subtracting these is like adding and subtracting different values. We just group the “like terms” (terms with the same variables and exponents) together then add or subtract. • 4x2y+2xy-3xy2+2x2y+2xy2-5xy • 4x2y+2x2y+2xy-5xy-3xy2+2xy2 • 6x2y-3xy-xy2 Multiplication • We have done this before actually, just on a smaller scale. We used FOIL for quadratics. We do something similar. If it is 2 values multiplied by 2 values, we do FOIL. If its more, then we distribute each value to the other group. Example • (x+y-z)(2x2-yz+y+z) • x(2x2-yz+y+z)+y(2x2-yz+y+z)-z(2x2-yz+y+z) • 2x3-xyz+xz+2x2y-y2z+y2+yz-2x2z+yz2-yz-z2 – Now we combine like terms • 2x3-xyz+xz+2x2y-y2z+y2+yz-2x2z+yz2-yz-z2 • There are no like terms, so this is as simple as we will get it. • Notice that FOIL is just distributing with two numbers.