Question

Find the remainder when x cube minus x square + 6 X + a is divided by x minus a

Answer 1

Here, p(x)=x

Here, p(x)=x 3

Here, p(x)=x 3 +ax

Here, p(x)=x 3 +ax 2

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is a

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a 2

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a 2 +6×a−a

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a 2 +6×a−a =2a

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a 2 +6×a−a =2a 3

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a 2 +6×a−a =2a 3 +5a

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a 2 +6×a−a =2a 3 +5a So, by the Remainder Theorem, 2a

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a 2 +6×a−a =2a 3 +5a So, by the Remainder Theorem, 2a 3

Here, p(x)=x 3 +ax 2 +6x−a, and the zero of x−a is aSo, p(a)=a 3 +a×a 2 +6×a−a =2a 3 +5a So, by the Remainder Theorem, 2a 3 +5a is the remainder when x

3

3 +ax

3 +ax 2

3 +ax 2 +6x−a is divided by x−a

Answer 2

Answer:

Let the polynomial be =

Let the polynomial be =p(x) = x³-ax²+6x-a

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-a

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :Consider g(x) = 0

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :Consider g(x) = 0x-a=0

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :Consider g(x) = 0x-a=0x = a

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :Consider g(x) = 0x-a=0x = aPut x = a in p(x)

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :Consider g(x) = 0x-a=0x = aPut x = a in p(x)p(x) = x³-ax²+6x-a

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :Consider g(x) = 0x-a=0x = aPut x = a in p(x)p(x) = x³-ax²+6x-a= a³-a×a²+6a-a

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :Consider g(x) = 0x-a=0x = aPut x = a in p(x)p(x) = x³-ax²+6x-a= a³-a×a²+6a-a= 5a

Let the polynomial be =p(x) = x³-ax²+6x-aThen g(x) = x-aTo Find : It's remainder when p(x) is divided by g(x) .Solution :Consider g(x) = 0x-a=0x = aPut x = a in p(x)p(x) = x³-ax²+6x-a= a³-a×a²+6a-a= 5aThe required remainder = 5a