Factoring Polynomials and Expressions

This video tutorial from Khan Academy focuses on factoring higher degree polynomials. It begins with a warm-up exercise on factoring quadratic expressions and progresses to more complex examples. The tutorial demonstrates how to factor expressions that are already partially factored and introduces the method of factoring by grouping. The video provides step-by-step guidance, encouraging viewers to pause and attempt the problems independently before reviewing the solutions together.

What is the first step in factoring the expression 6x² + 9x?

• Factor out a 2x

• Factor out a 6x

• Factor out a 3x

• Factor out a 9x

Which of the following is a perfect square trinomial?

• x² - 2x + 1

• x² + 2x + 1

• x² + 4x + 4

• x² - 4x + 4

What is the result of factoring x² - 4?

• (x - 2)(x + 2)

• (x - 4)(x + 4)

• (x - 2)²

• (x + 2)²

What technique is suggested for factoring x³ - 4x² + 6x - 24?

• Factoring by completing the square

• Factoring by trial and error

• Factoring by grouping

• Factoring by substitution

When factoring by grouping, what is the common factor in the terms x³ and -4x²?

• x

• x³

• 4x

• x²

What is the common factor in the terms 6x and -24?

• 3

• 24

• 6

• 12

After factoring by grouping, what expression is factored out from both groups?

• x² - 6

• x - 4

• x + 4

• x² + 6

What is the final factored form of x³ - 4x² + 6x - 24?

• (x + 4)(x² - 6)

• (x - 4)(x² - 6)

• (x - 4)(x² + 6)

• (x + 4)(x² + 6)

Which method is used to factor a polynomial with four terms?

• Factoring by substitution

• Factoring by trial and error

• Factoring by grouping

• Factoring by completing the square

What is the purpose of factoring a polynomial?

• To simplify the expression

• To find the roots of the polynomial

• To change the degree of the polynomial

• To expand the polynomial