Algebra 2 & Trigonometry REGENTS REVIEW

Questions and Answers

What should you do when raising a negative number to a power?

Always put the negative number in parentheses.

How do you factor the expression ax² + bx + c?

Factor by finding two numbers that multiply to ac and add to b.

What is the process of factoring by grouping?

Group terms together in pairs and factor out the common factors.

What can be done with terms that are opposite in signs?

They can be crossed out and replaced by a negative 1. Signup and view all the answers

How do you factor out a -1?

Remove the negative and change the signs of the terms. Signup and view all the answers

What are some strategies for performing operations with fractions?

Find a common denominator, then perform the operation. Signup and view all the answers

What are complex fractions?

Fractions where the numerator, denominator, or both contain fractions. Signup and view all the answers

How do you solve equations with fractions?

Find a common denominator, drop the denominators, and solve the resulting equation. Signup and view all the answers

What is the quadratic formula used to find the roots?

x = (-b ± √(b² - 4ac)) / (2a) Signup and view all the answers

What does completing the square involve?

Rearranging and adding a constant to form a perfect square trinomial. Signup and view all the answers

What can the discriminant tell you about the roots of a quadratic equation?

If the discriminant is 0, the roots are real, rational, and equal. If negative, the roots are complex or imaginary. If a perfect square, the roots are real, rational, and unequal. If not a perfect square, the roots are real, irrational, and unequal. Signup and view all the answers

What are the formulas for the sum and product of the roots?

Sum is -b/a, product is c/a. Signup and view all the answers

How do you solve absolute value inequalities?

Isolate the absolute value, change the inequality sign and the right term signs, and determine the solution set based on the original sign. Signup and view all the answers

Study Notes

Raising a Negative Number to a Power

Use parentheses when raising a negative number to a power to ensure proper calculation.

Factoring ax² + bx + c

Factor quadratic expressions by finding two numbers that multiply to (ac) and add to (b).

Factoring by Grouping

Group terms in pairs, factor out the common factor from each pair, and then factor out the common binomial.

Canceling Out Opposites

Opposite sign terms can be eliminated by crossing them out and replacing with (-1).

Factoring Out a -1

To factor out a (-1), remove the negative from the expression and change the signs of all terms involved.

Operations with Fractions

Combine fractions by finding a common denominator before performing addition, subtraction, multiplication, or division.

Complex Fractions

A fraction where the numerator, the denominator, or both are also fractions, requiring simplification by eliminating inner fractions.

Equations with Fractions

To solve, first find a common denominator, eliminate the denominators, solve the simplified equation, and check for extraneous solutions.

Quadratic Formula (Finding the Roots)

The quadratic formula is (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}), used to find the roots of a quadratic equation.

Completing the Square

A method to transform a quadratic equation into vertex form by adding and subtracting the square of half the coefficient of (x).

Discriminant (Describing the Roots)

If the discriminant ((b^2 - 4ac)) is:
- 0: real, rational, equal roots
- Negative: complex or imaginary roots
- Perfect square: real, rational, unequal roots
- Not a perfect square: real, irrational, unequal roots

Sum and Product of Roots

For a quadratic (ax^2 + bx + c):
- Sum of the roots: (-\frac{b}{a})
- Product of the roots: (\frac{c}{a})
- Can be expressed as (x^2 - (\text{sum})x + \text{product} = 0).

Absolute Value Inequalities

To solve:
- Isolate the absolute value expression.
- Change the inequality sign and the signs of the terms on the right side.
- Use "or" between solutions if the inequality has a greater than sign.
- Retain the original direction of the inequality if it has a less than sign.

Description

Prepare for the Algebra 2 & Trigonometry Regents exam with these flashcards. Each card covers essential concepts such as handling negative numbers, factoring polynomials, and simplifying expressions. Mastering these topics will boost your confidence and readiness for the test.