polynomials

Question

The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=−2. It goes through the point (5,56).
Find a formula for P(x).

Answer 1

P(x) = a(x-1)²(x)(x+2) is a polynomial of degree 4 and its roots are 1, 0 and -2, with multiplicity two for the first of them.

Also, P(5) = 556.  Substitute 5 into factored form above, and you'll soon know what the constant 'a' is.  DONE!

Answer 2

 

P(x) = A(x-1)²(x)(x+2)

 

56 = P(5) = A(5-1)²(5)(5+2) = A(16)(5)(7) = A(560)

A = 56/560 = 1/10

 

P(x) = (1/10) (x-1)² x (x+2)

Answer 3

P(x) = A * (x - 1)² * (X) * (x + 2)

 

It contains the point (5, 56)

 

P(5) = 56 = A * 4² * 5 * 7 = 560A

   A = 0.1

 

The polynomial is P(x) = 0.1 (x - 1)² * (x) * (x + 2)

                                 = 0.1x⁴ - 0.3x²  + 0.2x