Factoring Special Cases

What is the factored form of x² - 16?

• (x - 2)(x + 2)

• (x - 4)(x + 4)

• (x - 8)(x + 8)

• (x - 1)(x + 1)

What is factoring in algebra?

• Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

• Factoring is the method of adding two or more expressions together to form a new expression.

• Factoring involves finding the roots of a polynomial equation.

• Factoring is the technique of simplifying an expression by removing all variables.

What is the factored form of a² - b²?

• (a - b)(a + b)

• (a - b)²

• (a + b)²

• a² - b²

What is the importance of practicing factoring special cases?

• It helps students recognize patterns and apply the appropriate formulas quickly and accurately in problem-solving.

• It allows students to avoid learning complex mathematical concepts.

• It is only useful for advanced mathematics courses.

• It has no real-world application.

How can you identify a perfect square trinomial?

• A perfect square trinomial has all positive coefficients.

• A perfect square trinomial can be identified if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

• A perfect square trinomial is always a sum of squares.

• A perfect square trinomial has three distinct linear factors.

What is the role of the zero product property in factoring?

• It states that if the product of two factors is zero, then at least one of the factors must be zero.

• It is used to find the greatest common factor of two numbers.

• It helps in simplifying fractions before factoring.

• It determines the sum of the roots of a polynomial.

What are special cases in factoring?

• Specific patterns or formulas used to factor certain types of polynomials, such as perfect squares and the difference of squares.

• General rules that apply to all types of polynomials.

• Only applicable to linear equations.

• Methods used to simplify fractions.

What is the general approach to factoring polynomials?

• Identifying common factors, applying special case formulas, and simplifying the expression into its factors.

• Using the quadratic formula to find roots of the polynomial.

• Graphing the polynomial to find intercepts and factors.

• Substituting values to check for roots and then factoring based on those values.

How do you factor a perfect square trinomial?

• Using the formula a² + 2ab + b² = (a + b)² or a² - 2ab + b² = (a - b)².

• By applying the difference of squares formula: a² - b² = (a + b)(a - b).

• By grouping the terms and factoring out the common factor.

• By using the quadratic formula to find the roots.

What is the difference of squares formula?

• a² - b² = (a - b)(a + b)

• a² + b² = (a - b)(a + b)

• a² - b² = (a + b)(a + b)

• a² - b² = (a - b)(a - b)