Question

Solve the polynomial by factoring. 4x3 + 25x2 + 6x a , 0, -6 b -3 , 0, -6 c - \large \frac{1}{3}, 0, -3

Answer 1

Given:

The polynomial is

`4x^3+25x^2+6x`

To find:

The solutions of given polynomial by factoring.

Solution:

Let the polynomial be

`P(x)=4x^3+25x^2+6x`

It can be written as

`P(x)=x(4x^2+25x+6)`

Splitting the middle term, we get

`P(x)=x(4x^2+24x+x+6)`

`P(x)=x(4x(x+6)+1(x+6))`

`P(x)=x(x+6)(4x+1)`

For solutions,
`P(x)=0`.

`x(x+6)(4x+1)=0`

`x=0\text{ and }(x+6)=0\text{ and }(4x+1)=0`

`x=0\text{ and }x=-6\text{ and }x=-(1)/(4)`

Therefore, the solutions of given polynomial are 0, -6 and
`-(1)/(4)`. So, all options are incorrect because they are incomplete.