Answer: GIVEN : The expression is is divisible by TO FIND : The values of a and b by solving the given polynomials by Long Division method SOLUTION : Now divide the given polynomial x^4+x^3+8x^2+ax-bx 4 +x 3 +8x 2 +ax−b is divisible by x^2+1x 2 +1 x^2+1x 2 +1 can be written as x^2+0x+1x 2 +0x+1 x^2+x+7x 2 +x+7 ______________________ x^2+0x+1x 2 +0x+1 ) x^4+x^3+8x^2+ax-bx 4 +x 3 +8x 2 +ax−b x^4+0x^3+x^2x 4 +0x 3 +x 2 ___(-)___(-)__(-)_____________ x^3+7x^2+axx 3 +7x 2 +ax x^3+0x^2+xx 3 +0x 2 +x __(-)__(-)__(-)_____ 7x^2+(a-1)x-b7x 2 +(a−1)x−b 7x^2+0x+77x 2 +0x+7 _(-)___(-)__(-)___ (a-1)x-b-7 _________ The quotient is and remainder is (a-1)x-b-7 Since the the polynomial is completely divided by so that the remainder is zero ∴ (a-1)x-b-7=0 (a-1)x-b-7=0 can be written as (a-1)x+(-b-7)=0x+0 Now equating the coefficients of x and constant we get a-1=0 and -b-7=0 ∴ a=1 and b=-7 ∴ The values of a and b is 1 and -7 respectively. Reply
Answer:
GIVEN :
The expression is is divisible by
TO FIND :
The values of a and b by solving the given polynomials by Long Division method
SOLUTION :
Now divide the given polynomial
x^4+x^3+8x^2+ax-bx
4
+x
3
+8x
2
+ax−b is divisible by x^2+1x
2
+1
x^2+1x
2
+1 can be written as x^2+0x+1x
2
+0x+1
x^2+x+7x
2
+x+7
______________________
x^2+0x+1x
2
+0x+1 ) x^4+x^3+8x^2+ax-bx
4
+x
3
+8x
2
+ax−b
x^4+0x^3+x^2x
4
+0x
3
+x
2
___(-)___(-)__(-)_____________
x^3+7x^2+axx
3
+7x
2
+ax
x^3+0x^2+xx
3
+0x
2
+x
__(-)__(-)__(-)_____
7x^2+(a-1)x-b7x
2
+(a−1)x−b
7x^2+0x+77x
2
+0x+7
_(-)___(-)__(-)___
(a-1)x-b-7
_________
The quotient is and remainder is (a-1)x-b-7
Since the the polynomial is completely divided by so that the remainder is zero
∴ (a-1)x-b-7=0
(a-1)x-b-7=0 can be written as
(a-1)x+(-b-7)=0x+0
Now equating the coefficients of x and constant we get
a-1=0 and -b-7=0
∴ a=1 and b=-7
∴ The values of a and b is 1 and -7 respectively.