Factoring Polynomials: Techniques and Methods

This video tutorial reviews various methods of factoring polynomials, including the greatest common factor (GCF), factoring by grouping, basic and complex trinomials, and the difference of two squares. Each method is explained with examples, highlighting the steps and patterns involved in the factoring process.

What is the first step in any factoring problem?

• Identify the leading coefficient

• Check for the Greatest Common Factor (GCF)

• Split the polynomial into pairs

• Calculate the discriminant

What is the factored form of a polynomial when using the GCF method?

• The GCF times the difference of the remaining terms

• The product of the GCF and the polynomial

• The sum of the GCF and the remaining terms

• The GCF times the sum of the remaining terms

How do you factor a polynomial using the grouping method?

• Identify the leading coefficient

• Use the quadratic formula

• Multiply each term by the GCF

• Split into pairs and find the GCF of each pair

In the grouping method, what do you do after finding the GCF of each pair?

• Factor out the common binomial

• Divide the polynomial by the GCFs

• Multiply the pairs by their GCFs

• Add the GCFs together

What is required to factor basic trinomials?

• A difference of squares

• Four terms in the polynomial

• A leading coefficient of one

• A leading coefficient greater than one

How do you approach factoring trinomials when the leading coefficient is greater than one?

• Find the GCF first

• Split the middle term based on a*c and factor by grouping

• Use the quadratic formula

• Directly write the factors

For trinomials with a leading coefficient greater than one, what do you find to split the middle term?

• Factors of b minus c

• Factors of a plus c

• The square root of a times c

• Factors of a times c

What pattern do you check for when you have two terms being subtracted?

• Perfect square trinomials

• Difference of two squares

• Grouping method

• Basic trinomials

What is a key feature of the difference of two squares pattern?

• The GCF is subtracted from each term

• Both terms are perfect squares and subtracted

• It involves a leading coefficient greater than one

• The polynomial has three terms

What indicates a perfect square trinomial?

• A polynomial with four terms

• Three terms with a leading coefficient of one

• First and last terms are perfect squares and the middle term is twice the product of their square roots

• Two terms being subtracted