Question

How do you factorise the given equation $6{x^2} - 2x$?

Answer 1

Hint: First we will reduce the equation further if possible. Then we will try to factorise the terms in the equation. Split the middle term and factorise the equation. Then equate the factors equal to zero and evaluate the value of the variable.

Complete step by step answer:
We will start off by reducing any reducible terms in the equation.
$6{x^2} - 2x$
Now we will factorise the terms in the equation.
$
 \Rightarrow 6{x^2} - 2x \\
 \Rightarrow 6x(x - 2) \\
 $
Now we will equate the factors with zero.
$6x(x - 2) = 0$
Here, either $6x = 0$ or $x - 2 = 0$.
If we solve further, we will get,
$
\Rightarrow {x - 2} = 0 \\
\Rightarrow x = 2 \\
$
Hence, the values of $x$ are $0,2$.

Additional information: Factorisation consists of writing a number or another mathematical object as a product of several objects of the same kind. In particular, a univariate polynomial with complex coefficients admits a unique factorisation into linear polynomials; this is a version of the fundamental theorem of algebra.by the fundamental theorem of arithmetic, every integer greater than $1$ has unique factorisation into prime numbers, which are those integers which cannot be further factored into the product of integers greater than one.

Note: While splitting the middle term be careful. After splitting the middle term, do not solve all the equations simultaneously. Solve all the equations separately, so that you don’t miss any term of the solution. Check if the solution satisfies the original equation completely. If any term of the solution doesn’t satisfy the equation, then that term will not be considered as a part of the solution.