5. If the polynomial x-6+16x2-25x + 10 is divided by another polynomia

1.	5. If the polynomial x-6+16x2-25x + 10 is divided by another polynomial x2-2x+k,the remainder comes out to be x + a, find k and a.
Answer» LET x^4–6x³+16x²-25x+10 = q(x)(x²-2x+k)+(x+a)..【q(x≡ quotient 】 x^4–6x³+16x²-26x+(10-a) =(x²-2x+k)(x²-4x+m)【-6x³=-2x³-4x³】 Now,(i) comparing x-terms,2m+4k=26orm+2k=13...(A) (ii) comparing x²-terms ,m+k+8=16m+k=8m+2k=13 k=5m=3 BUT comparing constant terms, mk=10-a=15a=10–15=-5

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

Answer»

LET x^4–6x³+16x²-25x+10

= q(x)(x²-2x+k)+(x+a)..【q(x≡ quotient 】

x^4–6x³+16x²-26x+(10-a)

=(x²-2x+k)(x²-4x+m)【-6x³=-2x³-4x³】

Now,(i) comparing x-terms,2m+4k=26orm+2k=13...(A)

(ii) comparing x²-terms ,m+k+8=16m+k=8m+2k=13

k=5m=3

BUT comparing constant terms, mk=10-a=15a=10–15=-5