Advanced Factoring
What action can you take to bring an equation out of factored form and to the original?
Multiplying it out.
In synthetic division, what part of the dividend do you write down and use in the division?
The coefficients
What do you have to find before you can add/solve rational equations?
The LCD (Least Common Denominator)
What do you need to do before determining what the vertical asymptotes are in an equation?
Cancel out any terms possible from the numerator and denominator (find the holes).
When the difference between the degree of the numerator and denominator is greater than one, what do we end up with?
A backbone.
Using the quadratic formula, factor x2-12x-4.
x+/-18.3, x+/-5.7
When performing polynomial division, how do you write the remainder as a final solution?
Remainder over the original divisor.
X=4
How many cases do we have that will produce a horizontal asymptote?
2.
Find the slant asymptote of (x2+7x+8)/x-2.
X+9.
When you have more than one variable, how should you factor?
Factor by grouping.
Using synthetic division, solve (4x3-7x2-2x+3)/x+2.
4x2-15x+28-53/x+2
What is the second step when adding rational equations?
Isolating the numerator.
Find the Vertical Asymptotes of (2x+3)(x+6)(x-13)/x2+4x-12.
Vertical Asymptote at x=2.
When solving to find a backbone, what process do we use to solve?
Polynomial long division
Using the factoring algorithm, factor 4x2+7x+3.
(4x+3)(x+1)
Using polynomial long division, solve (x3+4x2-3x+4)/x2-3.
x+4+16/x2-3
Solve this rational equation for x: 1-3/x = 18/x2
x = 6, -3
Find the horizontal asymptotes of (x2+4x+7)/(x+3)(x+4).
Y=1.
Find the backbone of this equation: (x3-2x2-4x-7)/x+3
x2-5x+11-40/x+3