The denominator of a fraction (rational number) is the number on the bottom and indicates the total number of equal parts in the whole or the group. has denominator .
In a division problem, the dividend is the number or expression that is being divided.
In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression , 6 is the divisor and 152 is the dividend.
Polynomial long division
Polynomial long division is the standard method of long division, applied to the division of polynomials.
A rational expression is a fraction with polynomials in the numerator and the denominator.
Rational Root Theorem
The rational root theorem states that for a polynomial, , where are integers, the rational roots can be determined from the factors of and . More specifically, if is a factor of and is a factor of , then all the rational factors will have the form .
The remainder theorem states that if , then is the remainder when dividing by .
Synthetic division is a shorthand version of polynomial long division where only the coefficients of the polynomial are used.
Find the quotient and remainder of rational expressions that involve division.