Rational Functions Review

Operations with Rational Functions

100

Simplify: (5x+15)/(x+3)

What is 5?

200

Multiply: (a^2 + 7a + 12)/(a^2 - 9) x (a - 3)/(a+ 3)

What is (a + 4)/(a - 3)

300

Divide: (c^2 - c - 12)/(c^2 + 4c + 3) and (c^2 - 6c + 8)/(c^2 + 5c + 4)

What is (c + 4)/(c - 2)?

400

Subtract: (x)/(x-4) - (6x)/(x - 5)

What is (-5x^2 + 19x)/(x - 4)(x - 5)?

500

Solve: (3x + 6)/(x + 5) / (x + 2)/(x^2 - 25)

What is 3(x - 5)?

Randomness

100

Identify leading coefficient, degree, terms, and name for x³-18x²+2x-5

LC: 1, degree: 3, terms: 4, name: cubic polynomial

200

Identify real roots of x⁴-3x²-4 =0

What is x = -2, 2

300

Factor x⁶-14x⁴+49x²

What is x²(x²-7)(x²-7)

400

Using Rational Root Theorem, what are all possible rational roots for f(x)=x⁴+3x³-3x²-12x-4

What is +/-1, +/-2, +/-4

500

Describe graph's end behavior for P(x) = 2x³+3x²-4x

As x approaches -infinity, y approaches -infinity; As x x approaches +infinity, y approaches +infinity

Solving Rational and Radical Equations

100

Solve: SQRT (x) = 9

What is 81?

200

Solve: (x -2)/(x - 1) = x + 2

What is x = 0?

300

Solve: 5x -4 = -x² + 2

What is x = -6, 1?

400

Solve: SQRT(6x -5) = 5

What is x = 5?

500

Solve: (x^2 - 4)/(x + 3) + (x - 2)/(x + 3) = 2

What is x = 4?

Why do you have to be so Complex

100

Simplify i⁷

What is -i.

200

What is the conjugate for -6-5i?

What is -6+5i

300

What are the zeros for P(x)= x³+x

What are 0, i, and -i?

400

Simplify (2+i)(3-i²)

What is 2+i

500

Simplify 4-1 divided by 1+3i

What is 1/10 - 13/10i

Around the Room

100

Which row of Pascal's triangle gives coefficients for (a+b)⁴

What is 1 4 6 4 1?

200

Which specific pair of signs will factors be if quadratic has a +b and -c when in standard form?

What is + for larger factor and - for smaller factor?

300

Write a function when you are given that factors are x= 7, -6.

What is x²-x-42?

400

What is the third term of the expansion of (g²-2g)⁴?

What is 24g⁶

500

Simplify 5x⁶/x²y divided by 10x²/y

What is x²/2