Factoring Trinomials and Their Properties

This video tutorial covers the basics of factoring trinomials in the form of x^2 + bx + c, where the leading coefficient is 1. It explains the process of converting a trinomial from expanded form to factored form by identifying factors of the constant term that add up to the linear coefficient. The tutorial includes several examples to illustrate the process and also addresses more advanced techniques, such as factoring trinomials with non-unit leading coefficients by first identifying the greatest common factor.

What is the first step in factoring a trinomial where the leading coefficient is 1?

• Multiply the trinomial by a binomial.

• Find the greatest common factor.

• Write the trinomial in expanded form.

• Identify the factors of the constant term.

When factoring x^2 + 8x + 12, what are the factors of 12 that add up to 8?

• 2 and 6

• 1 and 12

• 4 and 8

• 3 and 4

In the trinomial x^2 - 4x - 32, what is the correct pair of factors for -32 that add to -4?

• -4 and 8

• -2 and 16

• -1 and 32

• -8 and 4

In the example x^2 + 28x + 75, which pair of factors of 75 adds up to 28?

• 1 and 75

• 3 and 25

• 5 and 15

• 10 and 7

When factoring x^2 - 4x - 32, why is it important to consider the signs of the terms?

• To ensure the product is positive.

• To determine the correct order of factors.

• To simplify the trinomial.

• To find factors that add to the middle term.

For the trinomial y^2 - 6y - 40, what are the factors of -40 that add to -6?

• -2 and 20

• -4 and 10

• -5 and 8

• -10 and 4

What is the first step when factoring a trinomial with a leading coefficient greater than 1?

• Write the trinomial in expanded form.

• Multiply the trinomial by a binomial.

• Factor out the greatest common factor.

• Find the factors of the constant term.

What is the result of factoring out the greatest common factor in the trinomial 3x^2 + 27x + 42?

• x^2 + 9x + 14

• 3(x^2 + 9x + 14)

• 3x(x + 9) + 14

• x^2 + 3x + 14

In the trinomial y^2 - 6y - 40, what is the significance of having one positive and one negative factor?

• It ensures the sum is negative.

• It balances the equation.

• It ensures the product is positive.

• It simplifies the trinomial.

What is the final step in factoring a trinomial with a leading coefficient of 1?

• Divide the factors to check the result.

• Add the factors to check the result.

• Subtract the factors to check the result.

• Multiply the factors to check the result.