Question

Using factor theorem, factorize each of the following polynomial:
x³-6x²+3x+10

Answer 1

The factorised polynomial is  $f(x)=x^3-6x^2+3x+10=(x+1)(x-2)(x-5)$

Step-by-step explanation:

Given polynomial is $x^3-6x^2+3x+10$

To factorise the given polynomial by Factor method :

Let f(x) be the given polynomial

Therefore $f(x)=x^3-6x^2+3x+10$

• Put x=1 in the above polynomial we get

$f(1)=1^3-6(1)^2+3(1)+10$

$=1-6+3+10$

$=14-6$

$=8\neq 0$

Therefore x-1 is not a factor

• Put x=-1 in the above polynomial we get

$f(1)=(-1)^3-6(-1)^2+3(-1)+10$

$=-1-6-3+10$

$=10-10$

$=0$

Therefore x+1 is a factor

By factor theorem " If f(x) is a polynomial and f(-1)=0 then x+1 is a factor of f(x) "

           $x^2-7x+10$

        __________________

  x+1) $x^3-6x^2+3x+10$

          $x^3+x^2$

        ___(-)__(-)____________

                 $-7x^2+3x$

                 $-7x^2-7x$

            __(+)__(+)_______

                            10x+10

                             10x+10

                       __(-)__(-)____

                                     0

                            _________

$f(x)=(x+1)(x^2-7x+10)$

$f(x)=(x+1)(x-2)(x-5)$

Therefore $f(x)=x^3-6x^2+3x+10=(x+1)(x-2)(x-5)$

By using the factor theorem we have factorised the given polynomial as (x+1)(x-2)(x-5)

Answer 2

Answer:

The factorised polynomial is  

Step-by-step explanation:

Given polynomial is  

To factorise the given polynomial by Factor method :

Let f(x) be the given polynomial

Therefore  

Put x=1 in the above polynomial we get

Therefore x-1 is not a factor

Put x=-1 in the above polynomial we get

Therefore x+1 is a factor

By factor theorem " If f(x) is a polynomial and f(-1)=0 then x+1 is a factor of f(x) "

           

       __________________

 x+1)  

         

       ___(-)__(-)____________

                 

                 

           __(+)__(+)_______

                           10x+10

                            10x+10

                      __(-)__(-)____

                                    0

                           _________

Therefore  

By using the factor theorem we have factorised the given polynomial as (x+1)(x-2)(x-5)

Step-by-step explanation: