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Question: Select the polynomial function with leading coefficient 4, degree 4, and zeros - 3, - 1, 0 and 52.


A ) f (x) = 4x4 + 6x3 + 28x2 + 30x
B ) f (x) = 4x4 + 6x3 - 28x2 - 60x
C ) f (x) = 4x4 + 6x3 + 28
D ) f (x) = 4x4 + 28x2 + 30

Steps to derive

1 The polynomial function with leading coefficient 4, degree 4, with -3, - 1, 0 & 52 as zeros is f (x) = 4(x + 3)(x + 1) (x - 0)(x - 52).

2 = 4 (x2 + 4x + 3) (x2 - 5x2)

3 = 2 (x2 + 4x + 3) (2x2 - 5x)

4 = 4x4 - 10x3 + 16x3 - 40x2 - 30x + 12x2 - 30x

5 f (x) = 4x4 + 6x3 - 28x2 - 60x.



Hence the right answer is Option B

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