Factorise by using factor theory : X^3-2x^2-5x+6

Question

Factorise by using factor theory :
X^3-2x^2-5x+6

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Skylar 7 months 2021-10-13T17:51:38+00:00 1 Answer 0 views 0

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    2021-10-13T17:53:29+00:00

    Answer:

    Step-by-step explanation:

    for a cubic equaiton you need to take guesses at first root so try 1 for x and we get 

    1^3 – 2(1^2) – 5(1) + 6 = 

    1 – 2 – 5 + 6 = 

    – 1 + 1 = 0 so 1 is a root and can be written as x – 1 now do long division 

    …………….x^2 – x – 6 

    …………….x^3 – 2x^2 – 5x + 6 

    x – 1………x^3 – x^2 

    …………………..- x^2 – 5x 

    ………………….- x^2 + x 

    …………………………..- 6x + 6 

    …………………………..- 6x + 6 

    so we have (x – 1)(x^2 – x – 6) as factors the second term can factored further and we get 

    (x – 1)(x – 3)(x + 2)

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