Given:
The polynomial is
[tex]4x^3+25x^2+6x[/tex]
To find:
The solutions of given polynomial by factoring.
Solution:
Let the polynomial be
[tex]P(x)=4x^3+25x^2+6x[/tex]
It can be written as
[tex]P(x)=x(4x^2+25x+6)[/tex]
Splitting the middle term, we get
[tex]P(x)=x(4x^2+24x+x+6)[/tex]
[tex]P(x)=x(4x(x+6)+1(x+6))[/tex]
[tex]P(x)=x(x+6)(4x+1)[/tex]
For solutions, [tex]P(x)=0[/tex].
[tex]x(x+6)(4x+1)=0[/tex]
[tex]x=0\text{ and }(x+6)=0\text{ and }(4x+1)=0[/tex]
[tex]x=0\text{ and }x=-6\text{ and }x=-\dfrac{1}{4}[/tex]
Therefore, the solutions of given polynomial are 0, -6 and [tex]-\dfrac{1}{4}[/tex]. So, all options are incorrect because they are incomplete.
