Unit 3 Precalc Review

Polynomial Division

100

2x+5 / x+1

2   Remainder 3 / x+1

200

2x³+x²-6x-8 / x-2

2x²+5x+4

300

3x⁴-5x²+3 /  x+2

3x³-6x²+7x-14    Remainder 31

400

(x⁴-16) / (x-2)

x³+2x²+4x+8

500

5x⁴-4x³+3x²-2x+1/x-3

5x³+11x²+36x+106

Remainder 319/x-3

Rational Expressions

100

What are the excluded values of the rational expression?

3/x-5

x≠5

200

Simplify:

x²-9/x²-3x

x+3/x

Excluded value: x≠3,0

300

2/x + 3/(x+1)

5x+2/x(x+1)

400

Simplify:

2/x ÷ 3/(x+1)

2(x+1) / 3x

500

Simplify

(1/x + 1/2) ÷ 1/4

(4/x) +2

U-Substitution

100

Solve:

x⁴-5x²+4=0

u=1 or 4

x=±1, ±2

200

Solve

x⁴-13x²+36=0

u= 9,4

x=±3,±2

300

Solve

x⁴-17x²+16=0

x²=16 or 1

x= ±4,±1

400

Solve

x⁴-10x²+9=0

x²=9 or 1

x= ±3,±1

500

x⁴-5x²-36=0

let 

u=x²

u=9 or -4

x=±3

Sigma Notation and Area Under a Curve

100

find the sum

4

Σ2n

n=1

20

200

Find the sum

5

∑(2n+1)

n=1

=35

300

Approximate the area under

f(x)=x+2

from x=0 to x=3 using 3 left-endpoint rectangles

A=9

400

Approximate the area under

f(x)=x²+1

from x=0 to x=2 using 4 right-endpoint rectangles

A=5.75

500

Write the following in sigma notation

1/2+4/3+9/4+16/5+25/6

5

Σn²/n+1

n=1

Linear and Non-linear Systems of Equations

100

Is this system linear or nonlinear

y=2x+3

y=-x+1

Linear

200

Predict the number of solutions

y=2x+1

y=-x+4

1 solution

300

Predict the number of solutions

y=3x-5

6x-2y=10

Infinite solutions

400

Is this system linear or nonlinear?

y=x²+1

y=-2x+3

Nonlinear

500

Predict the number of solutions:

y=x²

y=x+6

2 solutions 

(A parabola and a line intersect twice)