Polynomials

1. | Long Division | Synthetic Division |
Prepared by：Ivy Chua-Aganon

2. POLYNOMIALS
- an expression of more
than two algebraic
terms, especially the
sum of several terms
that contain different
powers of the same
variable(s).

3. = -7x + 6x3 - 12x5
= - 12x5 + 6x3 -7x

4. If you're dividing a polynomial by
something more complicated than just a
simple monomial (that is, by something
more complicated than a one-term
polynomial), then you'll need to use a
different method for the simplification.
That method is called "long polynomial
division", and it works just like the long
(numerical) division you did back in
elementary school, except that now
you're dividing with variables.
𝐱𝟐 − 𝟗𝐱 − 𝟏𝟎
𝒙 + 𝟏

5. x
x2 + 1x
- 10x
--
-
- 10
- 10
- 10x - 10
0
- + +

6. Synthetic division is a shorthand,
or shortcut, method of polynomial
division in the special case of
dividing by a linear factor and it
only works in this case.
Synthetic division is generally
used, however, not for dividing
out factors but for finding
zeroes (or roots) of polynomials.
More about this later.
First, write the coefficients
ONLY inside an upside-down
division symbol:
Put the test zero, x
= 1, at the left:
𝑥2 + 5𝑥 + 6
𝑥 − 1
1

7. 1
1
6
6
12
Remainder
Constant
x
Answer : x + 6

9. WRITTEN MATH (page 94)
B. Use synthetic division and long division method to find each
quotient.

12. Dont forget to check your GCR and anser your modules :))