Factoring Polynomials Quiz

Factoring Polynomials

Definition Factoring polynomials is the process of expressing a polynomial as a product of simpler polynomials.

Why Factor? Factoring is useful for:

• Simplifying expressions
• Solving equations
• Finding roots
• Graphing functions

Methods of Factoring

1. Greatest Common Factor (GCF)

• Find the GCF of all terms in the polynomial
• Divide each term by the GCF
• Write the polynomial as the product of the GCF and the resulting factors

2. Factoring by Grouping

• Divide the polynomial into groups of two terms each
• Factor out the common binomial from each group
• Combine the groups

3. Factoring Quadratic Expressions

• General form: ax^2 + bx + c
• Factoring: (x + r)(x + s), where r and s are constants
• r and s can be found by solving the equation ax^2 + bx + c = 0

4. Factoring by Decomposition

• Express the polynomial as the sum of squares or differences of squares
• Factor using the formulas:
  • a^2 + 2ab + b^2 = (a + b)^2
  • a^2 - 2ab + b^2 = (a - b)^2

5. Factoring by Synthetic Division

• Divide the polynomial by a linear factor (x - r)
• If the remainder is zero, then (x - r) is a factor

Common Factoring Mistakes

• Forgetting to factor out the GCF
• Overlooking common binomials
• Not checking for the existence of other factors

Tips and Tricks

• Look for common factors, especially the GCF
• Use the distributive property to expand and simplify
• Check your work by multiplying the factors back together

Factoring Polynomials

Definition and Purpose

• Factoring polynomials is the process of expressing a polynomial as a product of simpler polynomials.
• Factoring is useful for simplifying expressions, solving equations, finding roots, and graphing functions.

Methods of Factoring

Greatest Common Factor (GCF)

• Find the GCF of all terms in the polynomial.
• Divide each term by the GCF.
• Express the polynomial as the product of the GCF and the resulting factors.

Factoring by Grouping

• Divide the polynomial into groups of two terms each.
• Factor out the common binomial from each group.
• Combine the groups to obtain the factored form.

Factoring Quadratic Expressions

• The general form of a quadratic expression is ax^2 + bx + c.
• The factored form is (x + r)(x + s), where r and s are constants.
• r and s can be found by solving the equation ax^2 + bx + c = 0.

Factoring by Decomposition

• Express the polynomial as the sum of squares or differences of squares.
• Use the formulas:
  • a^2 + 2ab + b^2 = (a + b)^2
  • a^2 - 2ab + b^2 = (a - b)^2 to factor.

Factoring by Synthetic Division

• Divide the polynomial by a linear factor (x - r).
• If the remainder is zero, then (x - r) is a factor.

Common Factoring Mistakes

• Forgetting to factor out the GCF.
• Overlooking common binomials.
• Not checking for the existence of other factors.

Tips and Tricks

• Look for common factors, especially the GCF.
• Use the distributive property to expand and simplify.
• Check your work by multiplying the factors back together.