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Factorise x cube -2x square -5x plus 6

1 Answer

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Answer: {(x + 2), (x - 1), (x - 3)}

Explanation:

Presented symbolically, we have:

x^3 - 2x^2 - 5x + 6

Synthetic division is very useful for determining roots of polynomials. Once we have roots, we can easily write the corresponding factors.

Write out possible factors of 6: {±1, ±2, ±3, ±6}

Let's determine whether or not -2 is a root. Set up synthetic division as follows:

-2 / 1 -2 -5 6

-2 8 -6

-----------------------

1 -4 3 0

since the remainder is zero, we know for sure that -2 is a root and (x + 2) is a factor of the given polynomial. The coefficients of the product of the remaining two factors are {1, -4, 3}. This trinomial factors easily into {(x -1), (x - 3)}.

Thus, the three factors of the given polynomial are {(x + 2), (x - 1), (x - 3)}

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