Algebraic Division

Question 1

Degree

Answer 1

The highest power of x in the polynomial

Question 2

Divisor

Answer 2

This is the thing you’re dividing by

Question 3

Quotient

Answer 3

The stuff that you get when you divide by the divisor (not including the remainder)

Question 4

Remainder

Answer 4

The bit that’s left over at the end (for AS math this will be a constant)

Question 5

The factor theorem

Answer 5

If you get a remainder of zero when you divide the polynomial F(X) by (x-a), then (x-a) must be a factor of f(x)

If f(x) is a polynomial, and f(a) = 0, then (x-a) is a factor of f(x)

Question 6

Method 1- Divide by subtracting multiples of the divisor

Answer 6

1. Subtract a multiple of (x-k) to get rid of the highest power of x
2. Repeat step 1 until you’ve got rid of all powers of x
3. Work out how many lumps of (x-k), you’ve subtracted, and read off the remainder.

Question 7

Method 2 - algebraic long division

Answer 7

Do exercises to remember

Question 8

Method 3 - formula f(x) = q(x)d(x) + r(x)

Answer 8

1. Work out degrees of quotient and remainder. Quotient degree = deg f(x) - deg d(x)
Deg r(x) < deg d(x)

2. Write division using above formula replacing q(x) and r(x) w general polynomials
3. Work out values of constants by substituting x value. And then doing x=0
4. Expand brackets and equate coefficients.
5. Write out division again replacing ABCE etc.