Answer:
1) x= -3, 3, 6
2) x= -3, -2, 0
Step-by-step explanation:
[tex]f(x)=x^3-6x^2-9x+54[/tex]
To factor this, we can use grouping
First we can factor the first pair and second pairs of terms
[tex]x^2(x-6)-9(x-6)[/tex]
As we have the same factor on each of these, we can combine the like terms to get
[tex]x^2-9(x-6)[/tex]
This can be factored into
[tex](x+3)(x-3)(x-6)[/tex]
This gives us the zeroes of
x= -3, 3, 6
[tex]f(x)=x^4+5x^3+6x^2[/tex]
To factor this one, we first need to factor out a term
[tex]x^2(x^2+5x+6)[/tex]
This is a quadratic equation that simplifies to
[tex](x^2)(x+2)(x+3)[/tex]
This gives the zeroes of
x= -3, -2, 0
