Algebra solutions: How to factorize a polynomial?

Factorization of polynomials in Algebra is the method of simplifying their forms into more comprehensive.

Take a look at the two examples explained below to understand better.

^{Example 1:-}

X²-9x+18

Here this polynomial can be simplified as follows:-

X²-9x+18

=x²-6x-3x+18

=x(x-6)-3(x-6)

^=(x-6)(x-3)

Hence, X²-9x+18=(x-6)(x-3).................(This is the factorized answer)

^{Example 2:-}

X³-4x²+5x-2

Here, this polynomial can be simplified as follows:

X³-4x²+5x-2

=x³-3x²-x²+2x+3x-2

=X³-3x²+2x-x²+3x-2

=x(x²-3x+2)-1(x²-3x+2)

=(x²-3x+2)(x-1)

=(x²-2x-x+2)(x-1)

={x(x-2)-1(x-2)}(x-1)

=(x-2)(x-1)(x-1)

Therefore, X³-4x²+5x-2=(x-2)(x-1)(x-1)…………………………(This is the factorized answer)