Question

Factor 2x^2 - 6x + 4 completely

Answer 1

Answer:

Step-by-step explanation:

Factor

2

out of

2

x

2

.

2

(

x

2

)

+

6

x

−

4

Factor

2

out of

6

x

.

2

(

x

2

)

+

2

(

3

x

)

−

4

Factor

2

out of

−

4

.

2

x

2

+

2

(

3

x

)

+

2

⋅

−

2

Factor

2

out of

2

x

2

+

2

(

3

x

)

.

2(

x

2

+

3

x

)

+

2

⋅

−

2

Factor

2

out of

2

(

x

2

+

3

x

)

+

2

⋅

−

2

.

2

(

x

2

+

3

x

−

2

)

Answer 2

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:

$\begin{array}{l}{2 x-4=0} \\\\ {x=\frac{4}{2}=2}\end{array}$

x - 1 = 0

x = 1

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