Rational Expressions
What is the critical first step when attempting to simplify a rational expression?
Factor the numerator and denominator completely.
What do we call a polynomial that has exactly two terms?
A binomial
The expression x2 - 36 is an example of this special factoring pattern
Difference of two squares
What value(s) of x make the rational expression 1/(x+5) undefined?
X=5
What is the term for the highest exponent of the variable in a single-variable polynomial?
The degree
Factor the difference of squares: x2 - 81.
(x - 9)(x + 9)
Multiply and simplify the following expression: {(x2-4)/(x-2)}*{1/(x+2)}
1
In the polynomial 5x3 - 2x2 + 8x - 7, what is the leading coefficient?
5
Factor the perfect square trinomial: x2 + 10x + 25
(x + 5)2
Add the rational expressions:(2/x)+(3/x2)
(2x+3)/x2
When a polynomial is written with its terms in descending order of their degrees, it is said to be written in this specific form.
Standard form
Factor the difference of squares with a leading coefficient: 4x2 - 49
(2x - 7)(2x + 7)
Solve the rational equation for x: (1/x)+1/2=3/4
X=4
What is the degree of the specific term -4x3y2?
5 (because you add the exponents of the variables: 3 + 2 = 5).
Factor the sum of cubes: x3 + 8.
(x + 2)(x2 - 2x + 4)