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Use the factor theorem to factorize x ^(...

Use the factor theorem to factorize `x ^(3) + x ^(2) - 4x -4` completely.

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To factorize the polynomial \( f(x) = x^3 + x^2 - 4x - 4 \) using the factor theorem, we will follow these steps: ### Step 1: Identify possible rational roots The possible rational roots of the polynomial can be found using the factors of the constant term (-4) and the leading coefficient (1). The factors of -4 are ±1, ±2, and ±4.
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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)

  • Using remainder theorem, the factors of the polynomial 2 x^(3) + 3 x^(2) - 9 x - 10 are

    A
    (x-2),(x-3),(2x+5)
    B
    (x-2),(x+1),(2x+5)
    C
    (x-2),(x-1),(2x-9)
    D
    (x-2),(x+4),(2x-9)

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