Question

Factor 24x^3y^2-4x^2y+84x^4 please show work

Answer 1

The given equation is :

`24x^(3)y^(2) -4x^(2)y +84x^(4)`

Now taking
`4x^(2)` common from all the terms, we get

`4x^(2) (6xy^(2) -y+21x^(2) )=0`

Writing the equation in standard form we get:

`21x^(2) +6xy^(2) -y=0`

Now we will use the formula of quadratic equations to solve this,

`x1,2 = \frac{-b+\sqrt{b^(2)-4ac }} {2a}` and

`x1,2 = \frac{-b-\sqrt{b^(2)-4ac }} {2a}`

Now putting a = 21, b = 6y² and c = -y and solving the equations, we get

`x=\frac{-6y^(2)+\sqrt{36y^(4)+84y }}{42}` and

`x=\frac{-6y^(2)-\sqrt{36y^(4)+84y }}{42}`