Question

What is the equivalent factored form of 12x4 – 42x3 – 90x2?

Answer 1

The factored form is
`6x^2(2x +3)(x-5)`

Explanation:

We need to write the equivalent factored form of given expression

Given expression is
`12x^(4)-42x^(3)-90x^(2)`

`12x^(4)-42x^(3)-90x^(2)`

Re-write the above expression as,

`6x^2(2x^2 - 7x - 15)` ......(1)

Now, Factor the
`2x^2 - 7x - 15`

`2x^2 +3x-10x - 15`

`x(2x +3)-5(2x+3)`

Take out the common term,

`(2x +3)(x-5)`

Now, put this equation (1)

`6x^2(2x +3)(x-5)`

Therefore,the factored form is
`6x^2(2x +3)(x-5)`