P- (Algebraic) long division, algebraic fractions & factor/ remainder theorem DF

Question 1

What are the 2 formats for long division answers and what do the letters stand for?

Answer 1

1) F(x) ÷ P (x) = Q(x) + (R ÷P (x))
2) F(x) = Q(x) x P(x) + R
Where R= remainder, P= Division & Q= result on top

Question 2

What should you remember when doing algebraic long division?

Answer 2

Place holders if needed

Question 3

In algebraic long division what are the steps?

Answer 3

1) Divide first value in original by first value in divider
2) Multiply entire divider by the result of step 1 & put underneath
3) Subtract original division by result of previous step
4) Divide first value of result of previous step by first value of divider
5) Repeat

Question 4

What should you do with algebraic fractions?

Answer 4

Factorise then cancel out

Question 5

What is remainder theorem?

Answer 5

If f(x) is ÷ by (x-a), and a is substituted into f(x), the result is the remainder

Question 6

What is factor theorem?

Answer 6

If f(a) = 0, remainder is zero and so (x-a) is a factor