Write the cubic polynomial function f(x) in expanded form with zeros 4, -2, and 1, given that f(-1)=-12

tun1ju2k1ki 2022-10-02 Answered
Write the cubic polynomial function f(x) in expanded form with zeros 4, -2, and 1, given that f(-1)=-12
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Answers (1)

Piper Pruitt
Answered 2022-10-03 Author has 9 answers
Given that f ( 1 ) = 12
The cubic polynomial function is
f ( x ) = k ( x a ) ( x b ) ( x c )
where a = 4 , b = 2 , c = 1 f ( x ) = k ( x + 4 ) ( x + 2 ) ( x 1 ) f ( 1 ) = k ( 1 + 4 ) ( 1 + 2 ) ( 1 1 ) 12 = k ( 3 ) ( 1 ) ( 2 ) 12 = 6 k k = 2
put the value in equation
f ( x ) = 2 [ ( x + 4 ) ( x + 2 ) ( x 1 ) ] = 2 [ ( x 2 + 2 x + 4 x + 8 ) ( x 1 ) ] = 2 [ x 3 + 5 x 2 + 2 x 8 ] f ( x ) = 2 x 3 + 10 x 2 + 4 x 16
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