Finite Math Examples
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute the possible roots one by one into the polynomial to find the actual roots. Simplify to check if the value is , which means it is a root.
Simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Simplify each term.
Raise to the power of .
Multiply by .
Simplify by adding and subtracting.
Subtract from .
Add and .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Next, find the roots of the remaining polynomial. The order of the polynomial has been reduced by .
Place the numbers representing the divisor and the dividend into a division-like configuration.
The first number in the dividend is put into the first position of the result area (below the horizontal line).
All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.
Simplify the quotient polynomial.
Subtract from both sides of the equation.
The polynomial can be written as a set of linear factors.
These are the roots (zeros) of the polynomial .