Question

x³-6x+4 =? How do I solve this? ​

Answer 1

Answer: (x−2)(x^2+2x−2)

Step-by-step explanation:

Factor x^3−6x+4

x^3−6x+4  = (x−2)(x^2+2x−2)

Answer 2

Let us consider the expression, x³ -6x +4

We are going to use the trial and error method to factorise this expression,

Let us consider the value of x to e 1.

When x = 1

(1)³ – 6(1) + 4

= 1 – 6 + 4

= -1

Therefore, x = 1 is not the required value.

When x = 2

(2)³ – 6(2) + 4

= 8 -12 + 4

= 12 – 12

= 0

Therefore, the value of the expression becomes 0 when the value of x is equal to 2.

Hence, (x-2) is a factor.

Now,

X³ – 6x + 4

= x³ – 2x² +2x² – 4x -2x +4

= x²(x-2) +2x(x-2) -2(x-2)

= (x-2)(x² +2x -2)

Therefore the given equation can also be written as,

(x-2)(x² + 2x - 2) = 0  

Since, the product of two expressions is 0, then the value of either of the expression must be 0.

Therefore, x-2 = 0

x = 2

Again, x² +2x – 2 = 0

Using Sridharacharya’s rule for solving quadratic equation we get,

x = -1 + i  

x = -1 – i

Therefore,

x = 2, -1 + i, -1 -i

This is the required answer.