Transcript Radical, Irrational, Too Complex to be Real!

Dividing Polynomials
Intro - Chapter 4.1
Dividing Polynomials
Using Long Division
Example 1:
QUOTIENT
DIVISOR
x 4x 3
2
x  2 x  2x  5x  6
3
2
 x  2x 
3
2
4x 5x
2
 4 x  8 x 
3x 6
 3x  6 
0
2
REMAINDER
DIVIDEND
Using Synthetic Division to Divide a Polynomial
by a Divisor x – r
3
2
Example 2: Divide
by
1x 2 x 0 6
COEFFICIENTS
OF THE
DIVIDEND
r
1
x  22 
2 8 16
4 8 10
COEFFICIENTS
OF QUOTIENT
** REMEMBER
PLACE
HOLDERS**
REMAINDER
2 1 2 0 6
2 8 16
2
1x
4 8 10
1 4x

x2
The final answer:
It Means …
x  2 x  6   x  2  x  4 x  8   10
3
2
2
Division Algorithm:
If f x  is divided by hx  then
DIVISOR
REMAINDER
f xx  hhx  qxx  r xx
DIVIDEND
QUOTIENT
Things to Remember
DIVISOR and the
 If the remainder is 0 then, the __________
QUOTIENT
______________
are factors of dividend.
 If a polynomial is divided by ___________,
 
xc
f c
then the remainder is __________
79
24
x

3
x
5
Example3: Find the remainder when
is divided by x + 1
 1
 3  1  5  1  3  5  7
 A polynomial function f  x  has a linear factor
79
24
 
f a 0
x – a if and only if ___________
 A polynomial of degree n has at most n
ROOTS OR ZEROS
distinct real ____________________.
Let f x  be a polynomial. If r is a real number that
satisfies any of the following statements, then r
satisfies any of the following statements:
 r is a ________
ZERO of the function f
 r is an ______________
x  intercept of the graph of the function f
f  x  0
x
_____
 ris a solution, or root of the equation ________
xr
___________ is a factor of the polynomial f(x)
Asst. #48 Sect 4.1 pg. 248-250
#1-8, 9, 18, 22, 23, 28, 39, 45, 47, 50,
51, 57, 59, 61, 64, 69