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Find the factors of f(x) given that x = 5 is a zero.
f(x) = x3 − 6x2 − x + 30.

(x − 5)(x + 3)(x − 2)
(x − 5)(x − 3)(x + 2)
(x + 5)(x − 3)(x + 2)
(x + 5)(x + 3)(x − 2)

Relax

Respuesta :

  • If x = 5 is a zero of the given polynomial, then,
  • (x - 5) is a factor of the polynomial. [Since, x = 5 or, x - 5 = 0]
  • Now, divide the polynomial with (x - 5) using long division method. (See the picture)
  • We get (x^2 - x - 6) as the quotient.
  • Now, factorise the above polynomial:
  • (x^2 - x - 6)
  • = (x^2 - 3x + 2x - 6)
  • = x(x - 3) + 2(x - 3)
  • = (x - 3)(x + 2)
  • Therefore, x^3 − 6x^2 − x + 30 = (x − 5)(x − 3)(x + 2)

Answer:

B.(x − 5)(x − 3)(x + 2)

Hope you could get an idea from here.

Doubt clarification - use comment section.

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