Factoring Trinomials and Expressions

The video tutorial explains the process of factoring trinomials, especially when the leading coefficient is greater than one. It covers the importance of expressing a trinomial as a product of two factors, the role of coefficients, and how to find factor pairs that satisfy specific conditions. The tutorial also demonstrates rewriting middle terms and using grouping to factor trinomials effectively.

What is the main goal when factoring a trinomial?

• To eliminate the variable

• To find the roots of the equation

• To write it as a product of two factors

• To simplify the expression

When a trinomial has a coefficient greater than 1 in front of the squared term, what should you do?

• Divide the entire expression by the coefficient

• Add the coefficient to the constant term

• Ignore the coefficient

• Use the coefficient in the factoring process

What two numbers are needed to factor the expression if they multiply to -12 and add to 4?

• 3 and -4

• 6 and -2

• 2 and -6

• 4 and -3

Why can't you directly write the factors as (x + 6)(x - 2)?

• Because it doesn't match the original expression

• Because the signs are incorrect

• Because the numbers are not correct

• Because it changes the value of the expression

What is the purpose of rewriting the middle term in the factoring process?

• To simplify the expression

• To change the expression's value

• To eliminate the middle term

• To make it easier to factor by grouping

What common factor is found in the terms 6x^2 and 6x?

• x

• 6

• x^2

• 6x

After factoring out the common factor from the first two terms, what is the resulting expression?

• 6x + 1

• x + 1

• 6x - 1

• x - 1

What is the common factor in the terms -2x and -2?

• 2

• -x

• x

• -2

What is the final factored form of the expression?

• (x + 2)(6x - 1)

• (x - 2)(6x + 1)

• (x - 1)(6x + 2)

• (x + 1)(6x - 2)

Why is it important to ensure the expression is correctly factored?

• To eliminate errors

• To find the roots easily

• To maintain the original expression's value

• To simplify calculations