Question

divide x4- 4x3 + 8x2 + 7x+ 10 by ( x - 2) and verify the division algorithm​

Answer 1

Step-by-step explanation:

p(x) = x^4-4x^3+8x^2+7x+10x

4

−4x

3

+8x

2

+7x+10

g(x) = x-2

on dividing p(x) by g(x) we have

quotient = x³-2x²+4x-1

remainder = 8

verification

dividend = divisor × quotient + remainder

x^4-4x^3+8x^2+7x+10x

4

−4x

3

+8x

2

+7x+10 =(x-2) ( x³-2x²+4x-1) +8

x^4-4x^3+8x^2+7x+10x

4

−4x

3

+8x

2

+7x+10 = x^4-2x^3+4x^2-x-2x^3+4x^2-8x+2 +8x

4

−2x

3

+4x

2

−x−2x

3

+4x

2

−8x+2+8

x^4-4x^3+8x^2+7x+10x

4

−4x

3

+8x

2

+7x+10 = x^4-4x^3+8x^2+7x+10x

4

−4x

3

+8x

2

+7x+10

Answer 2

Step-by-step explanation:

division algorithm,

dividend = quotient×divisor+remainder

x⁴-4x³+8x²+7x+10=(x³-2x²+4x+15)(x-2)+40

=x⁴-2x³+4x²+15x-2x³+4x²-8x-30+40

x⁴-4x³+8x²+7x+10=x⁴-4x³+8x²+7x+10

LHS=RHS,hence verified.