Question

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

Answer 1

multiplicity of 2...means ²
multiplicity of 1 means just ^1

so if the roots are at 2, 0, and -3

(x -2)(x-0)(x+3)

your leading coefficent goes in front

4(x -2)(x-0)(x+3)

now which has which multiplicity?

4(x -2)²(x-0)(x+3)

so your P(X) = 4(x -2)²(x-0)(x+3)

if you want to simplify...go ahead

Answer 2

thanks can you help me with this last one please

Use the Factor Theorem to find a factor of
P(x)=x^3−6x^2+10x−5.
as follows: Compute P(1) = and P(−1) = .

Conclude that________ is a factor of P(x)=x3−6x2+10x−5

i just need the last part