Download A2 – Section 5.5 Date

A2 – Section 5.5
Date_______________
The Remainder & Factor Theorems
There are ______ ways to divide polynomials; ______________________ and
_______________________. Long division always works, but synthetic division
only works for a ______________ whose leading coefficient is +1.
Long Division
1.
Rewrite the polynomial you’re dividing in _________________________.
Include ______ descending powers even in they are not in the original problem.
3.
4.
_____________ the term with the greatest exponent of the divisor.
_____________
_____________

________ the
2.
5.
Bring the next term down.
remainder
divisor
Ex 1 Divide.
a) (8y3 – 10y2 + 5y – 9)  (2y – 1)
to the answer polynomial.
b) (y4 + 2y2 – y + 5)  (y2 – y + 1)
Factor Theorem: x – h is a factor of f(x) _______________________ f(h) = 0.
Remainder Theorem:
If f(x) is divided by (x – h), then, the remainder equals f(h), ____________.
Synthetic Division: Uses _________________ to divide
1.
2.
3.
4.
Write the coefficients of the polynomial in ___________________
including all descending powers.
Bring down the first coefficient.
_______________
_______________
 The __________ number under the box is the remainder.
 The other numbers stand for the coefficients of the answer polynomial whose
greatest exponent, degree, is _______ less than the original.
Ex 2 Divide (x3 – x2 – 2x + 8) by (x – 1).
Ex 3 Factor f(x) = 3x3 + 13x2 + 2x – 8
given that f(-4) = 0.
Ex 4 One zero of the f(x) = 2x3 – 9x2 – 32x – 21 is x = 7. Find the other zeros.