Factoring Polynomials: Techniques and Strategies

The video tutorial covers the basics of factoring polynomials, starting with identifying the greatest common factor and recognizing special patterns like the difference of squares and perfect square trinomials. It provides examples of factoring polynomials and introduces the sum and difference of cubes, explaining their specific patterns. The tutorial also covers factoring by grouping, demonstrating how to handle polynomials with common monomials. Throughout, the instructor emphasizes the importance of recognizing patterns and memorizing them for efficient factoring.

What is the first step in factoring polynomials completely?

• Perform synthetic division

• Identify the greatest common factor

• Sketch the graph of the polynomial

• Apply the quadratic formula

Which pattern is used when you have a polynomial like x^2 - 9?

• Sum of squares

• Perfect square trinomial

• Difference of squares

• None of the above

In the expression 2y^5 - 18y^3, what is the greatest common factor?

• 2y^3

• y^3

• 18y^3

• 2y^2

What does the sum of cubes factor into?

• 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 correct factorization for x^3 + 64?

• x^3 + 64 cannot be factored

• (x - 4)(x^2 + 4x + 16)

• x + 4

• (x + 4)(x^2 - 4x + 16)

What is the cube root of 343?

• 5

• 7

• 9

• 11

What is the correct sign pattern for the difference of cubes?

• Same, same, plus

• Opposite, same, minus

• Same, opposite, plus

• Opposite, opposite, plus

How do you factor by grouping if you have 4 terms in a polynomial?

• Divide the polynomial by x

• Group the first two and the last two terms separately

• Factor out the GCF from all terms

• Use the quadratic formula

What should be the result when factoring x^3 - 3x^2 - 16x + 48 by grouping?

• (x - 3)(x^2 - 16)

• Cannot be factored by grouping

• (x + 3)(x - 4)(x + 4)

• (x - 3)(x + 4)(x - 4)

What is the greatest common factor in the polynomial 2z^2(8z^3 - 125)?

• 2z^2

• 8z^3

• 125

• None of the above