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Factoring
Solving
Domain & Range
Complex Fractions
100

If an expression is prime, what is it's GCF?

1

100

What is the zero product property?

Ff there is the product of factors on one side and 0 on the other side of an equation, then at least one of the factors must be equal to 0

100
Explain in your own words what restrictive values are and how they relate to domain and range.

Restrictive values are x values that cannot mathematically exist in a rational function as an input in the domain space. This restriction also determines the mapped limitations on the y values (range).

100

What is an LCD?



The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

200

What is the Greatest Common Factor for this expression?

-4x2 + 8x - 4

4

200

Solve for x:


0 = 4x3+x2-3x

x = 0, -1, 3/4

200

Find the domain of the function:

f(x) = 1/(3x-4) + x3/(3x) + 1

x cannot equal 0, 4/3

Domain: (-inf, 0)U(0,4/3)U(4/3, +inf)

200

Which of the following is equivalent to:


(1/(x-1) - 1/x)/(1/(x2-x))

a. 1

b. 2/(x-1)

c. x/(x-1)

d. x-x2

What is the LCD?

Are there any restrictions here?

a. 1

LCD = x2-x

restrictions: x =/= 1, 0

300

Factor completely:

18x + 33 - 6x2 = -11x3


 (6x+11)(3-x3)



Step By Step: https://tutorial.math.lamar.edu/Solutions/Alg/Factoring/Prob6.aspx

300
Find all possible solutions for x, if one of the roots of this polynomial is -8.


f(x) = x3+x2-46x+80 


Hint: can we use long division for x+8?

x = -8, 2, 5

300

What is the domain and range for? What are the restrictive values?


y = 500 * sqrt(x-5) / (x2-10x+25)

graph to find the range.

restrictive values: x cannot equal 5 and x must be greater than or equal to 5


Domain: (5, inf)

Range: (0, 11.104)

300

simplify the complex fraction:

Jiyoo will write the fraction :)

Jiyoo will write out the answer.

400
Factor completely:

w2(1+w2)(4w2-1)10 + 9w(1+w2)(4w2-1)7

w(1+w2)(8w-1)7(512w4-192w3+24w2-w+9)

400

Solve this equation:


x + 1 = (2x-7)/(x+5) - (5x+8)/(x+5)

x = -4

400

Simplify and find the restrictive values and domain for this rational function:

f(x) = ((x-1)(x-2))/sqrt((x2-1)*(2x2-8x+8))

Simplified:


f(x) = sqrt((x-1)/(2(x+1)))

restrictions: x cannot equal 1, -1, 2 and (x < -1 or x > 1)

Domain: (-inf, -1)U(1, 2)U(2, +inf)

400

simplify and identify any restrictions:

(x/10 - 1/(x+1) - 2/x)/ (1/2 - x/10) - 10/(4x2+4x)

(x2-10)/4x


x =/= -1, 0

(-inf, -1)U(-1,0)U(0, +inf)

500

Factor completely:

2t16-16t8-256

2(t-2)(t+2)(t2+4)(t8+8)

500

Two cars start out at the same spot. One car starts to drive north at 40mph and 3h later, the second car starts driving to the east at 60 mph. How long after the first car starts driving does it take for the two cars to be 500 miles apart?

Hint: distance between two points is D = sqrt((x1-x2)2+(y1-y2)2)

Can use calculator.


Car A travels for 8.871 hours. Car B travels for 5.871 hours.

https://tutorial.math.lamar.edu/Solutions/Alg/QuadraticApps/Prob2.aspx

500

Find the domain of the function: (EXTRA HARD)

f(x) = sqrt(x2-4) / (e5x+7 * (x-3))

Since the exponential function (ex) is always positive, the quantity e5x+7 is always positive. Therefore, it doesn't have any restrictive values. The only restrictions we have are that x2-4 >= 0, and x-2 cannot equal 0. 


This gives domain:

(-inf, -2] U [2, 3) U (3, +inf)

500

Tower of Complex Fractions.

Jiyoo will write out the fraction now :)

Jiyoo will share answer.