Math, asked by sareenais14, 1 year ago

When x^4 + 2x^3 + 8x^2 + 12x + 18 is divided by x^2 + 5, the remainder comes out to be px + q. Find p and q.

Answers

Answered by siddhartharao77
3

Answer:

p = 2, q = 3

Step-by-step explanation:

Let, f(x) = x⁴ + 2x³ + 8x² + 12x + 18 and g(x) = x² + 5.

Long Division Method:

x² + 5) x⁴ + 2x³ + 8x² + 12x + 18 (x² + 2x + 3

          x⁴            - 5x²

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

                     2x³ + 3x²  + 12x

                    2x³             + 10x

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

                                  3x²  +  2x + 18

                                  3x²           +  15

           

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

                                                2x +  3

Remainder = 2x + 3.

On comparing the remainder with px + q, we get

p = 2, q = 3.

Hope it helps!

Answered by mathsdude85
0

Let us  divide x⁴ + 2x³ + 8x² +12x +18 by x²+5. The division process is as follows:

x²+5 )x⁴ + 2x³ + 8x² +12x +18(x²+2x+3

  x⁴          +5x²

    (-)          (-)

    -------------------------

2x³+3x²+12x +18

  2x³       +10x

  (-)           (-)

     ---------------------------

 3x²    +2x+18

   3x²          +15

  (-)              (-)

   ---------------------------

 2x  + 3

We get the Remainder = 2x  + 3

Remainder given= px+q

px+q =  2x  + 3

p= 2 , q= 3

[Comparing coefficient of x and constant terms both sides]

Hence, the value of p is 2 & value of q is 3.

HOPE THIS WILL HELP YOU...

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