Given that:
Degree = 5
Leading coefficient = Negative
Zero's = x = - 1, x= 1 ( multiplicity 2) , x = 2 , x = 3
y - intercept = ( 0, - 3).
By using,
A polynomial in variable x is a function that can be written in the form f(x) = anxn + a n-1 x n-1 + . . . + a1x + a0 .
Where an , an-1 , . . . , a1 , a0 are constant.
To find the polynomial function:
Using above information,
x = - 1, x= 1 ( multiplicity 2) , x = 2 , x = 3 are the zeros of the polynomial function.
A zero's is an x - intercepts .
We know that,
Zeros of the polynomial say f(x) are x = a , x = b can be written as f(x) = ( x- a) ( x - b).
Say a polynomial f(x) ,
f(x) = ( x - ( -1) ) ( x - 1)2 ( x - 2) ( x - 3)
= ( x+ 1)( x - 1)2 ( x - 2) ( x - 3)
Assume that a is the leading coefficient of the polynomial .
Then,
f(x) = a ( x - ( -1) ) ( x - 1)2 ( x - 2) ( x - 3)
By using,
y - intercept = ( 0 , - 3) , that is , f( 0 ) = - 3 is given.
Plug x = 0 in the above polynomial ,
f( 0) = a ( 0 + 1 ) ( 0 - 1)2 ( 0 -2) ( 0 - 3)
-3 = 6a
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