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Sagot :
Root x= 3 of multiplicity 2, it means we can factor it with : (x-3)²
Root x = 1, of multiplicity 1, it means we can factor this polynomial with : (x-1)
Root x = -3, of multiplicity 2, it means we can factor this polynomial with : (x+3)²
Finally we get this expression : (x-3)²(x+3)²(x-1)
This expression is a polynomial of degree 5 but what is the y intercept of it ?
Basically, we need to replace x by zero and the value of the expression will be the y intercept :
let x = 0
then ,
(0-3)²(0+3)²(0-1) = 9*9*(-1) = -81 #-162
We need an y intercept of value = -162
Thus we simply need to multiply by 2, and finally f(x) = 2(x-3)²(x+3)²(x-1)
satisfies all the required condition
Good Luck
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