Question

Give examples of polynomials p(x) , g(x) , q(x) and r(x) , which satisfy the division algorithm and

1) deg p(x) = deg q(x)

2) deg q(x) = deg r(x)

3) deg r (x) = 0

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Answer 1

In the answers below,

p(x) is Dividend

g(x) is Divisor

q(x) is quotient

r(x) is remainder
______________

Answer 1.)

Let p(x) = 2x + 2 and g(x) = 2

Degree of p(x) is 1

Degree of g(x) is 0

q(x) = x + 1

Degree of q(x) is 1

r(x) = 0

Here,

Degree of p(x) = Degree of q(x)
________________________

Answer 2.)

Let q(x) = 5 and g(x) = 2

Degree of q(x) is 0

Degree of g(x) is 0

q(x) = 2

Degree of q(x) is 0

r(x) = 1

Degree of r(x) is 0

Here,

Degree of r(x) = Degree of q(x)
________________________

Answer 3.)

Let p(x) = x^2 + x + 2 and g(x) = x + 1

Degree of p(x) is 2

Degree of g(x) is 1

q(x) = x

Degree of q(x) is 1

r(x) = 2

Degree of r(x) = 0

Answer 2

example one

p ( x ) = k ( 5x^3-3x^2+7) ; q ( x ) = 5 x^3 - 3x^2 +7

example two

p ( x ) = x^4-7x^3+13x^2-5 ; q ( x ) = x^3-3x^2+x+2

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