Show that x+3 is a factor of f (x) = 3x^4-3x^3-36x^2

Question

Mathematics

Carley Murillo

5 March, 12:40

Show that x+3 is a factor of f (x) = 3x^4-3x^3-36x^2

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Answers (1)

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Moriah Sanford · Answer 1

F (x) = 3x^4 - 3x³ - 36x²

f (x + 3) = 3 (x + 3) ^4 - 3 (x + 3) ³ - 36 (x + 3) ²

f (x + 3) = 3 ((x + 3) (x + 3) (x + 3) (x + 3)) - 3 ((x + 3) (x + 3) (x + 3)) - 36 ((x + 3) (x + 3))

f (x + 3) = 3 ((x² + 6x + 9) (x² + 6x + 9)) - 3 (x² + 6x + 9) (x + 3) - 36 (x² + 6x + 9)

f (x + 3) = 3 (x^4 + 12x³ + 54x² + 108x + 81) - 3 (x³ + 9x² + 27x + 27) - 36 (x² + 6x + 9)

f (x + 3) = 3x^4 + 33x³ + 99x² + 27x - 162