find k so that x-1 is a factor of x^3 – 3x^2 + kx – 1

Question

find k so that x-1 is a factor of x^3 – 3x^2 + kx – 1

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Nick 3 years 2021-08-01T01:51:05+00:00 2 Answers 21 views 0

Answers ( )

  1. Eirian
    0
    2021-08-01T01:52:11+00:00
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    Answer:

    k = 3

    Step-by-step explanation:

    If x-1 is a factor of x³ – 3x² + kx – 1 then value of x is 1.

    f (x ) = x³ – 3x² + Kx – 1 , then

    plug 1 as x in the expression.

    • f ( 1) = ( 1)³ – 3 ( 1)² + k (1) – 1 = 0

    expand exponents

    • 1 – 3 + k – 1 = 0

    combine like terms

    • -3 + k = 0

    Add 3 to both side

    • k = 3
  2. thucuc
    0
    2021-08-01T01:52:21+00:00
    Reply

    Answer:

    { \bf {factor : { \tt{x - 1}}}} \\ x - 1 = 0 \\ x = 1 \\ { \tt{f(x) = {x}^{3} - {3x}^{2} + kx - 1}} \\ { \tt{f(1) : {(1)}^{3} - 3 {(1)}^{2} + k(1) - 1 = 0}} \\ { \tt{k - 3 = 0}} \\ { \tt{k = 3}}

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