if the polynomial x^4 -6x^2 -25x+ 10 is divided by another polynomial x^2- 2x + k the remainder comes out to be x+ a , find k and a About the author Mackenzie
Answer: The value of a for which (x 4 −x 3 −11x 2 +7x+a) is divisible by (x+3). We can find this by subtracting x=−3 in the polynomial and equate it to zero, since (x+3) is the root ( zero ) of the polynomial. ⇒(−3) 4 −(−3) 3 −11(−3) 2 +7(−3)+a=0 ⇒81+27+9(−11)−21+a=0 ⇒a=12. Hence, the answer is 12. Reply
Answer:
The value of a for which (x
4
−x
3
−11x
2
+7x+a) is divisible by (x+3).
We can find this by subtracting x=−3 in the polynomial and equate it to zero, since (x+3) is the root ( zero ) of the polynomial.
⇒(−3)
4
−(−3)
3
−11(−3)
2
+7(−3)+a=0
⇒81+27+9(−11)−21+a=0
⇒a=12.
Hence, the answer is 12.