Respuesta :
The factorization of the given equation [tex]2 x^{2}-6 x+4 \text { is }(2 x-4)(x-1)[/tex]
Solution:
We have been given an equation as follows:
[tex]2 x^{2}-6 x+4[/tex]
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:
[tex]\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}[/tex]
We can find the roots of the given equation as follows:
[tex]\begin{array}{l}{2 x-4=0} \\\\ {x=\frac{4}{2}=2}\end{array}[/tex]
x - 1 = 0
x = 1
Therefore, the factorization of the given equation is (2x - 4)(x - 1)
