Question

on dividing the polynomial x²- 3p X + 3p- 7 by X + 1 we get 6 as remainder then find the value of p ​

Answer 1

Step-by-step explanation:

Let, f(x) =x³ +px²+x+6 

      g(x) = 2x³ - x²+(p+3)x -6

Now , when we divide by (x -3) both equations give same remainder.

Let the remainder be 'r'.

So, When we substitute x = 3 . Then they give 'r' as the value.

So, f(3) → 3³ + p(3²) + 3 + 6 = r .

             ⇒ 27 + 9p + 9 = r

 

             ⇒ 36 +9p = r   - (i)

      g(3) → 2(3³) - 3² + 3(p+3) -6 = r

             ⇒ 54 - 9 + 3p + 9 -6 =r

             ⇒ 48 +3p = r   - (ii)

Now equate (i) & (ii).

 Then, 48 + 3p = 36 + 9p  ( r = r)

           48 - 36 = 9p - 3p

  

            12 = 6p

 

Therefore p = 2.

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Answer 2

Answer:

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