Title: Mathematics / 7 Algebraic Methods / 7.1 Algebraic Fractions

Q: How can you divide algebraic expression? eg: \(x^3 +2x^2 -17x +6 / (x-3)\)
A: Grid method:
Long division method:

Q: How can you factorise a cubic, quantic etc equations? eg \(2x^3 - x^2 - 18x -9\)
A: \(f(x) = 2x^3 - x^2 - 18x -9\)
\(f(-1) =2(-1)^3 + (-1)^2 - 18(-1) -9 = 8\) Does not equal 0
\(f(1) = 2(1)^3 + (1)^2 - 18(1) - 9 = -24\)         Does not equal 0
\(f(3) = 2(3)^3 + (3)^2 - 18(3) -9 = 0\)
So \((x-3)\) is a factor of \(2x^3 +x^2 -18x -9\)
(See grid method)
\(2x^2 + 7x +3 (x-3)\)
(+) 7
(×) 6
6,1
\((2x+6)(2x+1)(x-3) -- >(x+3)(2x+1)(x-3)\)