Answer:
1)
[tex]x^{3} - 3timesx -2 = 0[/tex]
2)
[tex]x^{3} - x^{2} - 6timesx[/tex]
Step-by-step explanation:
1)
A polynomial function of x can be represented as
[tex]f(x) = (x + 1)(x + 1)(x - 2)[/tex], if we put x = -1 / -1 / 2, then we will get x = 0.
Now,
[tex]f(x) = (x + 1)(x + 1)(x - 2) = (x^{2} + 2timesx + 1)(x - 2) = x^{3} + 2timesx^{2} + x - 2timesx^{2} - 4timesx -2 = x^{3} - 3timesx -2.[/tex]
2)
Similarly, this function must have to be valued 0 for x = -2, 0, 3
Let g(x) be the function.
Hence,
[tex]g(x) = (x + 2)(x - 0)(x - 3) = (x^{2} + 2timesx )(x - 3) = x^{3} + 2timesx^{2} - 3timesx^{2} -6timesx = x^{3} - x^{2} - 6timesx[/tex]
