Question

If f(x) =x⁴-2x³+3x²-ax-b when divided by x-1, the remainder is 6, then find the value of a + b

Answer 1

The value of a+b is -4

Step-by-step explanation:

• Given polynomial is $f(x)=x^4-2x^3+3x^2-ax-b$
• Also given that the polynomial f(x) when divided by x-1, the remainder is 6

To find the value of a+b in given polynomial  :

         $x^3-x^2+2x+(-a+2)$

        __________________

  x-1) $x^4-2x^3+3x^2-ax-b$

         $x^4-x^3$

        ___(-)__(+)____________

                 $-x^3+3x^2$

                 $-x^3+x^2$

           __(+)__(-)_______

                         $2x^2-ax$

                         $2x^2-2x$                    

                ____(-)__ (+)___________

                                 -ax+2x-b

                                 -ax+2x+a-2

                  ______(+)_(-)_(-)_(+)_____

                                              -b-a+2

                   ________________________

Since the given polynomial f(x) when divided by x-1, the remainder is 6

• Therefore  -b-a+2=6
• -(b+a)+2=6
• -(b+a)=6-2
• -(b+a)=4
• b+a=-4

Rewritting we get a+b=-4

Therefore the value of a+b is -4.

Answer 2

ANSWER :–

a + b = -4

EXPLANATION :–

GIVEN :–

• A Function f(x) =x⁴ - 2x³ + 3x² - ax - b .

• When function divided by x - 1 , So it gives 6 as remainder.

TO FIND :–

Value of a + b

SOLUTION :–

• To find remainder , we have to put x = 1 in given function.

• According to the question –

=> f(1) = 6

=> (1)⁴ - 2(1)³ + 3(1)² - a(1) - b = 6

=> 1 - 2 + 3 - a - b = 6

=> 4 - 2 - (a + b) = 6

=> 2 - (a + b) = 6

=> (a + b) = 2 - 6

=> a + b = -4

• Therefore , a + b = -4