Polynomial Functions fx x5 7x4 15x3 15x2 14x 8 Determi

Polynomial Functions f(x) = x^5 + 7x^4 + 15x^3 + 15x^2 + 14x + 8 Determine all zeroes & sketch the graph.

Solution

f(x) = x⁵+4x⁴+15x³+15x²+ 14x+8

f(x) = (x+1)(x+2)(x+4)(x²+1)

To find the zeroes we have to set f(x) = 0

(x+1)(x+2)(x+4)(x²+1)=0

x+1=0   , x+2=0   , x+4=0    , x²+1=0

x=-1,-2,-4

To find the y intercept we have to plug x=0

f(x)=(0+1)(0+2)(0+4)(0²+1) =1*2*4*1=8

Hence the y intercept is (0,8)