What is a 3rd degree polynomial function like f(0)=18 and whose zeros are -1, 2 ,and 3

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What is a 3rd degree polynomial function like f(0)=18 and whose zeros are -1, 2 ,and 3

Mathematics
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Your polynomial has the form: \[y=ax ^{3}+bx ^{2}+cx+d\] For f(0)=18 : your x=0 and y=18 \[y=a*0 ^{3}+b*0 ^{2}+c*0+d\] D=18 And the zeros are when your y=0 so , you have for x=-1 \[0=-a+b-c+d\] \[0=-a+b-c+18\] for x=2 \[0=8a+4b+2c+d\] \[0=8a+4b+2c+18\] for x=3 \[0=27a+9b+3c+d\] \[0=27a+9b+3c+18\] You need to solve this system of 3 equations to find a,b and c
you can do it with matrices or by elimination
thanks so much!!

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Try this:\[f(x) = k(x+1)(x-2)(x-3)\]\[f(0) = k\cdot1 \cdot (-2) \cdot (-3) = 6k = 18 \Rightarrow k = 3\]So\[f(x) = 3(x+1)(x-2)(x-3)\]

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