Factoring Polynomials in the Form x² + bx + c

The video tutorial explains how to factor polynomials in the form x^2 + bx + c, focusing on cases where the leading coefficient is 1. It covers the relationship between factoring and multiplying polynomials, providing examples to illustrate the process. The tutorial also addresses factoring when the constant term is negative and when both the linear and constant terms are negative, using visual aids like tables to enhance understanding.

What is the main focus of this lesson on factoring polynomials?

• Understanding the relationship between factoring and multiplying polynomials

• Factoring polynomials where a is not 1

• Learning to solve quadratic equations

• Exploring the history of polynomials

In the factoring process, what do p and q represent?

• The factors of the constant term c

• The coefficients of x^2

• The roots of the polynomial

• The values that add to b and multiply to c

When factoring x^2 + 7x + 10, what are the correct factors?

• (x + 7)(x + 10)

• (x + 1)(x + 10)

• (x + 2)(x + 5)

• (x + 3)(x + 4)

What is the result of factoring x^2 + 11x + 24?

• (x + 2)(x + 12)

• (x + 4)(x + 6)

• (x + 3)(x + 8)

• (x + 1)(x + 24)

If c is negative, what must be true about the factors?

• One factor must be positive and one must be negative

• Both factors must be negative

• Both factors must be positive

• The factors must be equal

In the example x^2 + 9x - 36, what are the correct factors?

• (x + 3)(x - 12)

• (x - 3)(x + 12)

• (x + 6)(x - 6)

• (x - 6)(x + 6)

When both b and c are negative, what is true about the factors?

• The larger factor is negative

• Both factors are negative

• The smaller factor is negative

• Both factors are positive

What are the factors of x^2 - 4x - 21?

• (x + 7)(x - 3)

• (x - 7)(x + 3)

• (x - 3)(x + 7)

• (x + 3)(x - 7)

In the example x^2 - 4x - 21, why is the larger factor negative?

• Because b is positive

• Because the polynomial is quadratic

• Because c is positive

• Because both b and c are negative

What is the factored form of x^2 - 2x - 35?

• (x + 7)(x - 5)

• (x - 7)(x + 5)

• (x + 5)(x - 7)

• (x - 5)(x + 7)