2.369221

# The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x=-4. Its lead coefficient is 3. Find a formula for P(x)?

The factored formula for the polynomial is, (x - 3)(x - 3)x(x + 4) = 0, given that it has two equal roots when x = 3, a further root when x = 0 and another when x = -4.

This expands to x

As the lead coefficient is 3 then multiply all terms by 3.

3x

Then P(x) = 3x

This expands to x

^{4}- 2x^{3}- 15x^{2}+ 36x = 0As the lead coefficient is 3 then multiply all terms by 3.

3x

^{4}- 6x^{3}- 45x^{2}+108x = 0Then P(x) = 3x

^{4}- 6x^{3}- 45x^{2}+108x [or P(x) = 3x(x^{3}- 2x^{2}- 15x + 36)]