given that (x-1) is a factor of 5x^3 - 9x^2 + 2x + a find the value of a.

Question

it's a problem of factorising polynomial, what will be the value of a pls tell me..     :)

Answer 1

(x-1) is a factor of 5x^3 - 9x^2 + 2x + a, find the value of a.

 

1 | 5  -9   2     a

          5  -4    -2        

     5  -4  -2 | a-2 = 0

 

a = 2

 

Check:

 

5x^3 - 9x^2 + 2x + 2 =?

 

(x - 1)(5x^2 - 4x - 2) =

           ^^^^^^^^^^ is quotient of synth. div.

 

x(5x^2 - 4x - 2) - 1(5x^2 - 4x - 2) =

 

5x^3 - 4x^2 - 2x

        - 5x^2 + 4x + 2 =

 

5x^3 - 9x^2 + 2x + 2   √

Answer 2

Hi Rodela;

5x^3 - 9x^2 + 2x + a

(x-1)(...)

FIRST must be 5x²(x)=5x³

SECOND must be [-4x(x)]+[(-1)(5x²)]=-9x²

THIRD must be 4x+[(-1)(2x)]=2x

FOURTH must be (-1)(-2)=2

(x-1)(5x²-4x-2)

x(5x²-4x-2)=5x³-4x²-2x

-1(5x²-4x-2)=...-5x²+4x+2

5x³-9x²+2x+2

a=2

 

Just in case you need the information...

THIS IS THE WAY IT FACTORS INTO TWO PARENTHETICAL EQUATIONS.

For the FOIL...

FIRST must be (5x²)(x) or (x²)(5x).

OUTER must be (x²)(-9).

INNER must be (0.4)(5x) to result in 2x.

LAST must be (0.4)(-9) to result in -3.6

(x²+0.4)(5x-9)

Let's FOIL...

FIRST...(x²)(5x)=5x³

OUTER...(x²)(-9)=-9x²

INNER...(0.4)(5x)=2x

LAST...(0.4)(-9)=-3.6

5x³-9x²+2x-3.6

 

a=-3.6

 

 

Answer 3

 F( X ) =  5 X^3 -9 X^2 + 2X + a

 

 F( x ) has factor of X -1 , then  X =1 is zero of the polynomial:

 

       0 = 5 (1) ^3 - 9 ( 1) ^2 + 2 ( 1) + a

 

       0 = 5 - 9 + 2 + a

 

      a = 2

 

      Test:                 5x^2 - 4X -2                        

                X - 1  l 5X^3 - 9X^2 + 2X +2

                           5x^3 +5x^2            

                                    -4x^2 +2x

                                    - 4x^2- 4x       

                                              - 2x +2

                                              -2x  +2

                                                0

       5 x^3 -9 x^2 + 2x + 2 = ( x-1) ( 5x^2- 4x - 2)