ABSTRACT
Before looking at long division in algebra let us revise long division with numbers (we may have forgotten, since calculators do the job for us!). For example,
208 16
is achieved as follows:
13 ——–
16 )
208 16 48 48 —
· · —
(1) (2) 16 divided into 20 goes 1 (3) Put 1 above the zero (4) Multiply 16 by 1 giving 16 (5) Subtract 16 from 20 giving 4 (6) Bring down the 8 (7) 16 divided into 48 goes 3 times (8) Put the 3 above the 8 (9) 3× 16 = 48
(10) 48− 48 = 0
Hence 208 16
= 13 exactly Similarly,
172 15
is laid out as follows:
11 ——–
15 )
172 15
22 15 —
7 —
Hence 172 15
= 11 remainder 7 or 11+ 7 15
= 11 7 15
Below are some examples of division in algebra, which in some respects is similar to long division with numbers. (Note that a polynomial is an expression of the form
f (x) = a + bx + cx2 + dx3 + ·· · and polynomial division is sometimes required when resolving into partial fractions – see Chapter 21)
Problem 1. Divide 2x2 + x − 3 by x − 1
2x2 + x − 3 is called the dividend and x − 1 the divisor. The usual layout is shown below with the dividend and divisor both arranged in descending powers of the symbols.
