Factoring Polynomials and GCF

The video tutorial explains how to factor expressions completely by first identifying and factoring out the greatest common factor. It covers two examples: factoring 2n^3 + 128 using the sum of cubes formula and factoring x^8 - 216x^5 using the difference of cubes formula. The tutorial provides step-by-step guidance on identifying perfect cubes and applying the appropriate formulas to achieve the correct factored form.

What is the first step in any factoring problem?

• Identify the sum of cubes

• Factor out the greatest common factor

• Rewrite the expression

• Check for perfect squares

What is the greatest common factor of 2n^3 + 128?

• 4

• 8

• 2

• n

Which formula is used to factor n^3 + 64?

• Difference of squares

• Quadratic formula

• Difference of cubes

• Sum of cubes

In the expression n^3 + 64, what is the value of b?

• 16

• 2

• 8

• 4

What is the binomial factor of n^3 + 64?

• n - 16

• n + 4

• n + 16

• n - 4

What is the greatest common factor of x^8 - 216x^5?

• x^8

• x^5

• x^3

• 216

What is the value of b in the expression x^3 - 216?

• 12

• 3

• 6

• 18

Which formula is used to factor x^3 - 216?

• Sum of cubes

• Difference of squares

• Quadratic formula

• Difference of cubes

What is the binomial factor of x^3 - 216?

• x + 6

• x - 36

• x - 6

• x + 36

What is the trinomial factor of x^3 - 216?

• x^2 - 12x + 36

• x^2 + 6x + 36

• x^2 - 6x + 36

• x^2 + 12x + 36