Chapter 2: Polynomials

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Polynomials CBSE NCERT Solutions

Question:

If the polynomial x4 – 6x+ 16x2 - 25x + 10  is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.

Answer:

Solution: We have P(x) = x4 – 6x+ 16x2 - 25x + 10

And remainder = x + a.

Now we can divide P(x) = x4 – 6x+ 16x2 - 25x + 10 by x2 – 2x + k.

 

 

According to question

(-9 + 2k)x  + 10 – 8k + k2 =  + a

On comparing the like coefficients, then we have

 -9 + 2k = 1 and 10 – 8k + k2 = a

 –10 + 2k = 0  and  10 – a – 8k + k2 =  0

 k = 10/2 = 5  and  10 – a – 8 (5) + 52 = 0

 k = 5  and   – a – 5 = 0

 k = 5  and   a  =  –5

Hence, k = 5 and a = -5.

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