Question

x3-10x2–53x-42 factorise it​

Answer 1

Answer:

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Answer 2

p(x) = x^3- 10 x^2 - 53 x - 42

p(-1) = (-1)^3 - 10 (-1)^2 - 53(-1) - 42

= -1 - 10 + 53 - 42

= -11 -11 = 0

So p(-1) is a factor of the given equation.

since x+1 = -1

x= -1

therefore x+1 is a factor of x^3 - 10x^2 - 53x - 42

by using long division we get,

x+1 ) x^3 - 10 x^2 - 53 x - 42 ( x^2-11 x - 42

       x^3 +  x^2

      (-)      (-)

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

                - 11 x^2 - 53 x

                - 11 x^2 - 11 x

                (+)         (+)

                -------------------

                              - 42 x - 42

                              - 42 x - 42

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

                                     0

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

By factorisation method

(x^2 - 11 x - 42)(x+1)

(x^2 - 14 x + 3 x - 42)(x+1)

[x(x-14)+3(x-14)(x+1)

(x+3)(x-14)(x+1)