Question

factorise : 2x^3-3x^2-17x+30

Answer 1

Answer:

Given :- Factorise : 2x^3-3x^2-17x+30

(X-2)(x+3)(2x-5)

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Step-by-step explanation:

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Answer 2

Given,

The polynomial 2x³-3x²-17x+30 is given.

To find,

We have to find the factors of the given polynomial 2x³-3x²-17x+30.

Solution,

The factors of the polynomial 2x³-3x²-17x+30 are (x-2), (x+3), (2x-5).

We can simply factorize the given polynomial 2x³-3x²-17x+30 by finding its one root by the hit and trial method.

Substituting x = 2 in the given polynomial, we get

p(2) = 2(2)³-3(2)²-17(2)+30

      = 16- 3(4)-34+30

      = 46-46

      = 0

We get (x-2) the factor of the polynomial.

Now by synthetic division of the polynomial 2x³-3x²-17x+30 by 2, we get

the depressed equation 2x²+x-15.

Factorize the depressed equation by splitting the middle term, we get

            2x²+6x-5x-15

            2x(x+3)-5(x+3)

            (x+3)(2x-5)

which is the required factorization of the polynomial 2x³-3x²-17x+30.

Hence, 2, -3, 5/2 are the required roots of the equation, and (x-2), (x+3), (2x-5) are the required factors.