Factoring Polynomials A
Factor x2 - y2
(x-y)(x+y)
True or False
x + 2 is a factor of x2 - 4
True
Because the factors of x2 - 4 are (x+2) and (x-2)
What are the rules in identifying if a given expression is rational or NOT?
No variable under a radical sign
variables should not have a negative or fractional exponent
the denominator should not be equal to zero
What value of x will make the expression x over (4 - x) undefined?
To be undefined, the denominator must be zero.
The denominator is 4 - x, if the b=value of x is 4 the denominator will be 4-4 which is equal to zero.
So, the answer is 4.
Factorable or NOT:
x2 + 4
Not Factorable
What are the factors of 3x3 + 9x2?
3x2(x + 3)
What is the value of 2x2 over 3y if x=3 and y = 2?
2 (3)2 over 3 (2)
2 (9) over 6
18 over 6 or 18 divided by 6
The answer is 3
If the expression is already in its simplest form, what is the common factor of the numerator and denominator?
1
What polynomial has factors (x+5)(x-1)?
x2 + 4x -5
What polynomial has factors
(2x2 + 2) and (4x4 - 4x2 + 4)?
8x6 + 8
Sum of Two Cubes
Simplify:
15x2y5
--------
30x3y3
Answer:
y2
---
2x
Simplify:
x2 + 4
--------
x + 2
Answer:
x2 + 4
--------
x + 2
since x2 + 4 is NOT Factorable anymore.
True or False
6x2 - 11x - 10 = (3x + 2)(2x - 5)
True
Because if you multiply
(3x + 2) and (2x - 5) using FOIL METHOD you will get 6x2 - 11x - 10
If x - y is one of the factors of x3 - y3, what is the other factor?
x3 - y3 is Difference of Two Cubes
The factors are (x - y) and (x2 + xy + y2)
How many 20x/y are there in 40x/y2 ?
40x 20x 2
------ divided by ------ =-----
y2 y 7
What is the product of (3x - 3) over 2y2 and y over (6x - 6)?
1 over 4y
If the area of a square lot is given by the polynomial (x2 + 6x + 9) square meters, what is the length of a side?
(x2 + 6x + 9) is a perfect square trinomial, therefore it can be factored as (x + 3)2 or (x + 3) (x + 3).
So the length of a side is (x + 3) meters
Factor completely: x4 - 16y4
x4 - 16y4 - Difference of Two Squares (DTS)
x4 - 16y4 = (x2 - 4) (x2 + 4)
but (x2 - 4y) can still be factored as (x - 2y)(x+2y) using DTS also. Therefore x4 - 16y4= (x - 2y)(x+2y) (x2 + 4y2).
Final Answer: (x - 2y)(x+2y) (x2 + 4y2)
What is the perimeter of a triangular lot whose sides are x/2, 3x/4 and 3x/2?
11x/4 units
If the length of a rectangular table is (x2 - 25)/(x+5) and the area is (x2 - 5x)/2x , then what is the measurement of the width?
1/2