# Long division

[br]If the degree of a polynomial expression is more than 2 and at least one of the factors is [br]known, long division can be used to find the rest of the factors. The method is quite similar to long division for numbers.[br][br][u][color=#0000ff]Example 3[/color].[/u] Divide 23456 by 123 with long division.[br]
[br][u][color=#0000ff]Example 4[/color].[/u] Solve the division $\Large \frac{6x^3+x^2-19x+6}{x+2}.$[br]
[br] [br][color=#0000ff][u]Example 5.[/u][/color] Factorize $\Large 6x^3+x^2-19x+6.$ [br][br]From previous example we know that [br][br][br] ﻿$\Large 6x^3+x^2-19x+6=(x+2)(6x^2-11x+3).$ ﻿[br][br][br]By finding the zeros for the quadratic expression, we can factorize the expression further[br][br][br] ﻿ ﻿$\Large 6x^3+x^2-19x+6\\[br]\Large=(x+2)6(x-\frac{3}{2})(x-\frac{1}{3})\\[br]\Large=(x+2)(2x-3)(3x-1)$[br][br][br] [br]