Math Jeopardy

Advanced Factoring

100

What action can you take to bring an equation out of factored form and to the original?

Multiplying it out.

200

Using the quadratic formula, factor x²-12x-4.

x+/-18.3, x+/-5.7

300

When you have more than one variable, how should you factor?

Factor by grouping.

400

Using the factoring algorithm, factor 4x²+7x+3.

(4x+3)(x+1)

Division

100

In synthetic division, what part of the dividend do you write down and use in the division?

The coefficients

200

When performing polynomial division, how do you write the remainder as a final solution?

Remainder over the original divisor.

300

Using synthetic division, solve (4x³-7x²-2x+3)/x+2.

4x²-15x+28-53/x+2

400

Using polynomial long division, solve (x³+4x²-3x+4)/x²-3.

x+4+16/x²-3

Solving Rational Equations

100

What do you have to find before you can add/solve rational equations?

The LCD (Least Common Denominator)

200

Solve this rational equation for x: 4/2x + (6+x)/x = 12/x

X=4

300

What is the second step when adding rational equations?

Isolating the numerator.

400

Solve this rational equation for x: 1-3/x = 18/x²

x = 6, -3

Vertical and Horizontal Asymptotes

100

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).

200

How many cases do we have that will produce a horizontal asymptote?

2.

300

Find the Vertical Asymptotes of (2x+3)(x+6)(x-13)/x²+4x-12.

Vertical Asymptote at x=2.

400

Find the horizontal asymptotes of (x²+4x+7)/(x+3)(x+4).

Y=1.

Oblique Asymptotes

100

When the difference between the degree of the numerator and denominator is greater than one, what do we end up with?

A backbone.

200

Find the slant asymptote of (x²+7x+8)/x-2.

X+9.

300

When solving to find a backbone, what process do we use to solve?

Polynomial long division

400

Find the backbone of this equation: (x³-2x²-4x-7)/x+3

x²-5x+11-40/x+3