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Using the factor theorem, show that (x-2...

Using the factor theorem, show that `(x-2)` is a factor of `x^(3) +x^(2) -4x -4`. Hence factorise the polynomial completely.

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Using the factor theorem, show that (x-2) is a factor of 3x^(2)-5x-2 . Hence factorise the given expression.

Using the Factor theorem, show that (i) (x-2) is a factor of x^(3)-2x^(2)-9x+18 . Hence factorise the expression x^2-2x^2-9x+18 completely. (ii) (x+5) is a factor of 2x^3+5x^2-28x-15 . Hence factorise the expression 2x^3+5x^2-28x-15 completely. (iii) (3x+2) is a factor of 3x^(3)+2x^(2)-3x-2 . Hence factorise the expression 3x^3+2x^2-3x-2 completely.

Knowledge Check

  • Using the remainder theorem the factors of the polynomial x^(3) + x^(2) - 4 x - 4 are

    A
    (x+1),(x-2),(x-2)
    B
    (x-1),(x+1),(x+2)
    C
    (x+1),(x+1),(x-2)
    D
    (x+1),(x+2),(x-2)

  • If x^(2)-4 is a factor of polynomial x^(3)+x^(2)-4x-4 , then its factors are:

    A
    `(x-2)(x+2)(x+1)`
    B
    `(x-2)(x+2)(x-1)`
    C
    `(x-2)(x-2)(x+1)`
    D
    `(x-2)(x-2)(x-1)`

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