Question

Factor 2x^2 - 6x + 4 completely

Answer 1

The factorization of the given equation
`2 x^(2)-6 x+4 \text { is }(2 x-4)(x-1)`

Solution:

We have been given an equation as follows:

`2 x^(2)-6 x+4`

We need to completely factorize it.

According to the definition of factorization we understand, a polynomial can be written as a product of two or more polynomials of degree less than or equal to that of it.

The process involved in breaking a polynomial into the product of its factors is known as the factorization of polynomials.

So, we factorize the equation according to the definition as follows:

`\begin{array}{l}{=2 x^(2)-6 x+4} \\\\ {=2 x^(2)-2 x-4 x+4} \\\\ {=2 x(x-1)-4(x-1)} \\\\ {=(2 x-4)(x-1)}\end{array}`

We can find the roots of the given equation as follows:

`\begin{array}{l}{2 x-4=0} \\\\ {x=(4)/(2)=2}\end{array}`

x - 1 = 0

x = 1

Therefore, the factorization of the given equation is (2x - 4)(x - 1)