Question

factorize x^3-6x^2+3x+10

Answer 1

okay u just have to split the successive terms . or just make it zero and try to find roots we can easily see that -1 is root .

Answer 2

The factorization of the polynomial $x^{3} - 6x^{2} +3x+10$ is (x+1)(x-2)(x - 5).

Step-by-step explanation:

• When a polynomial is factored, its prime factorization is used to break it down into the product of two or more other polynomials. Polynomials can be easily simplified with the aid of factoring. Each term of the longer expression should first be written as the product of its elements. The similar elements among the phrases are then removed in order to create the necessary factors as a second stage. The key principles involved in factoring polynomials as well as the ways for doing so are GCF, the long division formula, and the remainder theorem.
• According to the given information, it is given that the polynomial is $x^{3} - 6x^{2} +3x+10$.

Putting the value of 5 for x in the above polynomial, we get,

5³-(6*5²)+(3*5)+10 = 125 - 150 + 15 + 10 = 150 - 150 = 0.

Thus, (x - 5) is a facto of this polynomial.

Dividing the polynomial by (x-5), we get,

x-5 ) $x^{3} - 6x^{2} +3x+10$ ( x² -x -2

       x³  - 5x²

      -      +

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

               -x²  + 3x + 10          

               -x²  + 5x

               +     -

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

                      -2x + 10

                      -2x + 10  

                     +      -

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

                               0

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

Thus, x² -x -2 is another factor of the polynomial.

Now, x² -x -2 = x² - 2x + x -2 = x( x - 2) + 1(x - 2) = (x+1)(x-2)

Thus, the factorization of the polynomial $x^{3} - 6x^{2} +3x+10$ is

(x+1)(x-2)(x - 5).

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