## Quick Reference

A method of finding the quotient and remainder when a polynomial *f*(*x*) is divided by a factor *x*−*h*, in which the numbers are laid out in the form of a table. The rule to remember is that, at each step, ‘you multiply and then add’. To divide *ax*^{3}+*bx*^{2}+*cx*+*d* by *x*−*h*, set up a table as follows:

Working from the left, each total, written below the line, is multiplied by *h* and entered above the line in the next column. The two numbers in that column are added to form the next total:

The last total is equal to the remainder, and the other numbers below the line give the coefficients of the quotient. By the Remainder Theorem, the remainder equals *f*(*h*).

For example, suppose that 2*x*^{3}−7*x*^{2}+5*x*+11 is to be divided by *x*−2. The resulting table is:

So the remainder equals 9, and the quotient is 2*x*^{2}−3*x*−1. The calculations here correspond exactly to those that are made when the polynomial is evaluated for *x*=2 by nested multiplication, to obtain *f*(2)=9.

*Subjects:*
Mathematics.

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