Core 4 - Dividing Polynomials

Question 1

Method for finding remainder when:

x^3 -3x^2 =2x +7)/(3x+2

Answer 1

Solve 3x+2=0 => x=-2/3
Find f(-2/3) to find remainder.

Question 2

Method for proving factor of f(x)

Answer 2

Solve equation to find value for x
fing f(x) using substitution
If f(x)=0, then the expression is a factor of f(x)

Question 3

For polynomial division, what relationship between the exponents must be the case?

Answer 3

The numerator must have a higher exponent than the denominator.

Question 4

What are the steps for polynomial division?

Answer 4

Divide the largest exponent by the first term of the expression,
Multiply the result by the expression,
Subtract this from the corresponding terms in the original equation.
Carry down the next term, and start again, dividing the largest term from the subtraction by the expression.

Question 5

What is the benefit of re-writing p/q as a+(b/q)

Answer 5

It is easier to apply calculus to this than for two polynomials.

Question 6

Express 2x^2 -3x +4 /(x^2 + 5x -7) in the form A + (B/(x^2 + 5x -7))

Answer 6

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