Factoring
9x2-4
(3x-2)(3x+2)
Use long division to determine if (x+2) is a factor of (x3+4x2+5x+2)
(x3+4x2+5x+2) / (x+2) = x2+2x+1
therefore (x+2) is a factor
f(x) = x2 - 4x + 5
Find all the roots.
These have a 180 degree rotation about the origin and f(-x)=-f(x).
What are odd functions?
f(x)=(-6x5-2x+13)
g(x)=(4x5+3x2+x-9)
What is f(x)+g(x)?
-2x5+3x2-x+4
x3-3x2-5x+15
(x2-5)(x-3)
Use synthetic division to determine if (x+3) is a factor of 2x3+7x2-4
(x+3) is not a factor because 2x3+7x2-4 / (x+3) equals 2x2+x-3 remainder 5/x+3
f(x) = x3-3x2-10x
Find all the roots.
{-2, 0, 5}
A downturned parabola is an indication of these two characteristics.
What is an even degree and a negative leading coefficient?
f(x)=(-6x5-2x+13)
g(x)=(4x5+3x2+x-9)
What is f(x)-g(x)?
-10x5-3x2-3x+22
8c6-125
(2c2-5)(4c4+10c2+25)
Use the Factor Remainder Theorem to determine if (x-3) is a factor of f(x)=x4-6x2-10x+3.
(x-3) is a factor because f(3)=0
f(x) = x3+6x2+11x+6
One factor is (x+1). Use synthetic division to find the remaining factors. State the factored form and roots.
(x+1)(x+2)(x+3)
{-3, -2, -1}
Is y = (x-1)(x-6)2 odd, even, or neither?
Neither
Multiply:
(x+2)(x2-3x+5)
x3-x2-x+10
15x3-25x2+75x-125
5(x2+5)(3x-5)
Use the Rational Root Theorem to find all the possible factors of 3x2+2x2-x-2.
+-1, +-1/3, +-2, +-2/3
f(x) = 3x3+x2-x+1
Use the Rational Root Theorem to find all possible factors and synthetic division to find the factored equation. State the factored form and roots.
(x+1)(3x2-2x+1)
{-1, (1+i (21/2))/3, (1-i (21/2))/3}
Is y = x3-4x odd, even, or neither. Justify your answer.
Odd because:
f(-x)=-x3+4x
So f(-x)=-f(x)
Simplify:
(5x3+3x2+5)-(7x3-9x2+8x-5)
-2x3+12x2+8x+10
(2x3-4x2-3x-6)
prime (unfactorable)
If (x+2) is a factor of 2x3-7x+2, use synthetic division to find the factored equation.
(x+2)(2x2-4x+1)
The quadratic formula.
What is (-b+-(b2-4ac)1/2)/2a ?
What is the end behavior for f(x)=-2x3+2x2-x+5?
As x--->-infinity, f(x)--->+infinity
As x--->+infinity, f(x)--->-infinity
Simplify:
(3x-7)2-(2x2-12x+20)
7x2-30x+29