Factoring Techniques in Polynomials

The video tutorial covers various techniques for factoring polynomials, including using the greatest common factor (GCF), difference of squares, sum and difference of cubes, and factoring by grouping. It also introduces the concept of u substitution for more complex polynomials. The tutorial provides examples and exercises to help students understand and apply these methods effectively.

What is the first step you should take when factoring a polynomial?

• Look for a difference of squares

• Identify the sum of cubes

• Use u-substitution

• Find the greatest common factor

Which of the following is a correct application of the difference of squares formula?

• (x + 3)(x - 3) = x^2 + 9

• (x + 3)(x - 3) = x^2 - 9

• (x - 3)(x - 3) = x^2 - 6x + 9

• (x + 3)(x + 3) = x^2 + 9

What is the formula for the sum of cubes?

• a^3 + b^3 = (a - b)(a^2 + ab + b^2)

• a^3 + b^3 = (a + b)(a^2 - ab + b^2)

• a^3 - b^3 = (a + b)(a^2 + ab + b^2)

• a^3 - b^3 = (a - b)(a^2 - ab + b^2)

What is the result of factoring the expression x^3 - 1 using the difference of cubes formula?

• (x - 1)(x^2 + x + 1)

• (x + 1)(x^2 - x + 1)

• (x - 1)(x^2 - x + 1)

• (x + 1)(x^2 + x + 1)

When using u-substitution for factoring, what should 'u' typically represent?

• The highest power of the variable

• The constant term

• The coefficient of the leading term

• The most complex expression in the polynomial

Which technique is used when the second power is half the size of the first power in a trinomial?

• Factoring by grouping

• U-substitution

• Difference of squares

• Sum of cubes

What is the final step in the u-substitution method for factoring?

• Use the sum of cubes formula

• Apply the difference of squares formula

• Convert back to the original variable

• Leave the expression in terms of 'u'

Which of the following is a key step in factoring by grouping?

• Factor out the GCF from each pair of terms

• Combine all terms into a single expression

• Use the sum of cubes formula

• Apply the difference of squares formula

In the context of polynomial factoring, what does 'linear' mean?

• The polynomial has a degree of 1

• The polynomial is a constant

• The polynomial has a degree of 2

• The polynomial has no variables

What should you do if a polynomial has four terms?

• Apply the difference of squares formula

• Factor by grouping

• Use u-substitution

• Use the sum of cubes formula