dividend

Examples of dividend in the following topics:

• Dividing Polynomials

  • For example, find the quotient and the remainder of the division of $x^3 - 12x^2 -42$, the dividend, by $x-3$, the divisor.
  • The dividend is first rewritten like this: $x^3−12x^2+0x−42$.
  • The quotient and remainder can then be determined as follows: Divide the first term of the dividend by the highest term of the divisor (meaning the one with the highest power of $x$, which in this case is $x$): $x^3 \div x = x^2$.
  • For example, find the quotient and the remainder of the division of $x^3 - 12x^2 -42$, the dividend, by $x-3$, the divisor.
  • Divide the first term of the dividend by the highest term of the divisor (meaning the one with the highest power of $x$, which in this case is $x$): $x^3 \div x = x^2$.

• Division and Factors

  • So given two polynomials $D(x)$ (the dividend) and $d(x)$ (the divisor), we are looking for two polynomials $q(x)$ (the quotient) and $r(x)$ (the $remainder)$ such that $D(x) = d(x)q(x) + r(x)$ and the degree of $r(x)$ is strictly smaller than the degree of $d(x).$
  • So we write down a $3x^2$, multiply the divisor with this result and subtract this from the dividend:
  • This means that $D(x)=d(x)q(x)$: the dividend is a multiple of the divisor, or the divisor is said to $$divide the dividend.
  • We say that the divisor is a factor of the dividend.

• Negative Numbers

  • If the dividend and the divisor have the same sign, that is to say, the result is always positive.

• The Remainder Theorem and Synthetic Division

  • We start by writing down the coefficients from the dividend and the negative second coefficient of the divisor.

• Simplifying, Multiplying, and Dividing Rational Expressions

  • Recall the rule for dividing fractions: the dividend is multiplied by the reciprocal of the divisor.