The polynomial of degree 4, P ( x ) P ( x ) has a root of multiplicity 2 at x = 1 x = 1 and roots of multiplicity 1 at x = 0 x = 0 and x = − 3 x = - 3 .

Question

The polynomial of degree 4, P(x)P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=−3. It goes through the point (5,448)(5,448). 

Find a formula for P(x)P(x). 

P(x)= ?

Answer 1

P(x) = a(x-0)(x-1)²(x-(-3)) = ax(x+3)(x-1)² = a(x²+3x)(x²-2x+1) = a(x⁴ + x³ - 5x² + 3x)

Plug in 5 for x and set the polynomial equal to 448. Then solve for a.

Answer 2

P(x) = (x+3)x(x-1)

= (x^2+2x-3)x

= x^3 +2x^2 -3x

take each zero and change its sign, then stick an x in front of it

convert zero -3 to x+3, covert 1 to x-1, x-0= x

the multiply those factors together (x+3)(x-1)(x) to get P(x)