Factoring Polynomials and Expressions

This video tutorial covers the basics and advanced techniques of factoring polynomials, starting with quadratics and moving to higher degree polynomials. It introduces the concept of common factors, substitution, and differences of squares, providing examples and encouraging practice on Khan Academy. The tutorial aims to build a strong foundation in algebraic manipulation, preparing students for more complex mathematical challenges.

What is the common factor in the polynomial 3x^2 + 4x?

• x

• x^2

• 4

• 3

Which two numbers add up to 7 and multiply to 12 in the expression x^2 + 7x + 12?

• 2 and 6

• 1 and 6

• 3 and 4

• 2 and 5

How can you factor the expression x^2 - 9?

• (x + 3)(x - 3)

• (x + 1)(x - 1)

• (x + 2)(x - 2)

• (x + 9)(x - 9)

What is the first step in factoring the polynomial x^3 + 7x^2 + 12x?

• Divide by x

• Multiply by 2

• Add 1 to each term

• Factor out x

How can you rewrite a^4 + 7a^2 + 12 to make it easier to factor?

• (a^2 + 3)(a^2 + 4)

• a^2(a^2 + 7a + 12)

• a(a^3 + 7a + 12)

• (a + 3)(a + 4)

What is the factored form of 4x^6 - 9y^4?

• (2x^3 + y^2)(2x^3 - y^2)

• (x^3 + 3y^2)(x^3 - 3y^2)

• (4x^3 + 9y^2)(4x^3 - 9y^2)

• (2x^3 + 3y^2)(2x^3 - 3y^2)

How can you factor x^4 - y^4?

• (x^2 + y^2)(x + y)(x - y)

• (x^2 + y)(x^2 - y)

• (x + y)(x - y)

• (x^2 + y^2)(x^2 - y^2)

What is the result of factoring x^2 - y^2?

• (x + y)^2

• (x^2 + y^2)

• (x + y)(x - y)

• (x - y)^2

What is the purpose of recognizing patterns in algebra?

• To simplify expressions

• To make calculations harder

• To avoid solving problems

• To memorize formulas

Why is it important to practice factoring polynomials?

• To improve mathematical skills

• To memorize answers

• To skip algebra

• To avoid learning new topics