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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials1 Mark
MCQ
The factors of x3 - 7x - 6 are.
  • A
    x(x - 6) (x - 1)
  • B
    (x - 1) (x - 3) (x + 2)
  • C
    (x + 1) (x + 2) (x - 3)
  • D
    (x2 - 6) (x - 1)
✓

Answer

  1. (x + 1) (x + 2) (x - 3)
    Solution:
    The given expression to be factorized is x3 - 7x + 6
    This can be written in the form
    x3 - 7x + 6 = x3 - (1 + 6)x + 6
    = x3 - x - 6x + 6
    Take common x from the first two terms and -6 from the last two terms.
    Then we have,
    x3 + 7x + 6 = x(x2 - 1) - 6(x - 1)
    = x{(x)2 - (1)2} - 6{x - 1}
    = x(x + 1)(x - 1) - 6(x - 1)
    Finally, take common (x - 1) from the above expression,
    x3 - 7x + 6 = (x - 1) {(x + 1) - 6}
    = (x - 1) (x2 + x - 6)
    = (x - 1) (x2 + 3x - 2x - 6)
    = (x - 1) {x(x + 3) - 2(x + 3)}
    = (x - 1) (x + 3) (x - 2)

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