Algebra II

Advanced algebraic concepts including polynomials, rational expressions, and complex numbers.

Polynomials and Their PropertiesFactoring and Solving Polynomial EquationsRational Expressions and Equations
Complex Numbers and Their OperationsPolynomial Division and the Remainder TheoremPolynomial and Rational Inequalities
Modeling Real-World Data with PolynomialsApplications of Rational Expressions in Science and EngineeringComplex Numbers in Electrical Engineering and Art
Mastering Word ProblemsChecking Your SolutionsSmart Use of Calculators and Technology
Polynomials and Thei...Factoring and Solvin...Rational Expressions...Complex Numbers and ...Polynomial Division ...Polynomial and Ratio...Modeling Real-World ...Applications of Rati...Complex Numbers in E...Mastering Word Probl...Checking Your Soluti...Smart Use of Calcula...
Basic Concepts

Factoring and Solving Polynomial Equations

Breaking Down Equations

Factoring is like breaking a big LEGO structure into its pieces. In algebra, we write polynomials as the product of smaller polynomials. This helps us solve equations like \( x^2 + 5x + 6 = 0 \).

Common Factoring Techniques

  • Greatest Common Factor (GCF): Pull out what all terms share.
  • Trinomials: Find two numbers that add and multiply to certain values.
  • Difference of Squares: \( a^2 - b^2 = (a + b)(a - b) \).

Solving Equations

Once a polynomial is factored, set each factor equal to zero to find the solutions (roots).

Why Factor?

Factoring helps us solve equations that tell us when things like the height of a ball or the profit of a business will be zero.

Examples

  • \( x^2 + 5x + 6 = (x + 2)(x + 3) \), so the solutions are \( x = -2 \) and \( x = -3 \).

  • \( 2x^2 - 8 = 2(x^2 - 4) = 2(x + 2)(x - 2) \).

In a Nutshell

Factoring polynomials turns them into simpler pieces, making equations easier to solve.

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Rational Expressions and Equations