Factoring Techniques and Examples

This video tutorial reviews various factoring techniques, including GCF, grouping, difference of squares, type 1 and type 2 factoring, and factoring completely. It also covers the sum and difference of cubes, providing step-by-step instructions and examples for each method.

What is the first step in identifying the GCF of a polynomial?

• Combine like terms

• Identify the coefficients

• Divide by the smallest coefficient

• List all factors of each term

When factoring by grouping, what should you do after finding the GCF of the first two terms?

• Divide the polynomial by the GCF

• Write down what's left over after dividing

• Combine the terms into a single factor

• Identify the GCF of the next two terms

How do you handle the coefficients when factoring by grouping?

• Find the GCF of the coefficients

• Multiply them

• Subtract the smaller from the larger

• Add them together

What is a necessary condition for applying the difference of two squares technique?

• Both terms must be perfect squares

• The terms must be added

• The terms must have even exponents

• There must be more than two terms

What must be true about the terms in a difference of two squares?

• They must be divisible by two

• They must include a variable

• They must be added

• They must be subtracted

In Type 1 factoring, what relationship must the two numbers have?

• They must be the square roots of the constant term

• They must add to the coefficient of x squared

• They must multiply to the middle term

• They must multiply to the constant term and add to the coefficient of x

What additional step is involved in Type 2 factoring compared to Type 1?

• Multiplying the coefficient of x squared by the constant

• Finding the square root of the leading coefficient

• Subtracting the constant from the product of the coefficients

• Adding the coefficients of x squared and x

What is the first step in factoring a sum of cubes?

• Identify the cube root of each term

• Square each term

• Divide each term by three

• List all factors of each term

What sign is used in the trinomial part of the sum of cubes factorization?

• Opposite of the first term's sign

• Always plus

• Same as the first term's sign

• Always minus

In the context of advanced factoring techniques, what does 'same opposite always plus' refer to?

• The signs used in the sum and difference of cubes

• The method for finding the GCF in complex polynomials

• The sequence of operations in Type 2 factoring

• The pattern of coefficients in quadratic equations