(please show me how to do this!) A polynomial f (x) and one of its zeros are given. Use Polynomial Division to find the remaining the zeros, and write f(x) in factored form.

Question

f(x) = x^3 + 6x^2 - 19x - 84. -7 is a zero.

Answer 1

(-7)^3 + 6*(-7)^2 - 19(-7) - 84 =

-343 + 294 + 133 - 84 =

-49 + 133 - 84 =0

-7 | 1 6 -19 -84

-7 7 84

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1 -1 -12 0

x^2 - x - 12 = 0

( x - 4 )( x + 3 ) = 0

x= 4 or x = -3

the solution set is {-7, 4, -3 }

checks x = -4

4^3 + 6* 4^2 - 19*4 - 84 =

64 + 96 - 76 - 84 = 0

checks x=-3

(-27) + 54 + 57 - 84 = 0