Factoring Trinomials and Binomials

The video tutorial explains how to factor a trinomial with a lead coefficient of one. It begins by introducing the concept of a lead coefficient and the quadratic term. The tutorial then guides viewers through the process of writing the factors of a trinomial, which are binomials. It emphasizes the importance of finding numbers that multiply to the last term and add to the middle term of the trinomial. The example used involves finding factors of -10 that add up to -3, leading to the factors (x + 2) and (x - 5). The video concludes with a practical example to reinforce the learning.

What is the lead coefficient in a trinomial?

• The number in front of the x term

• The number in front of the x squared term

• The constant term

• The sum of all coefficients

What is the first step in factoring a trinomial?

• Simplifying the expression

• Writing the trinomial as a product of two binomials

• Finding the greatest common factor

• Solving for x

What should the first term in each binomial be when factoring x^2?

• x^2

• x

• 0

• 1

What two conditions must the numbers meet when factoring a trinomial?

• They must both be positive

• They must multiply to the last term and add to the middle term

• They must be even numbers

• They must be prime numbers

Which pair of numbers multiplies to -10 and adds to -3?

• 2 and -5

• 5 and -2

• -1 and 10

• 1 and -10

Why can't 1 and -10 be the correct factors for the trinomial?

• They are not integers

• They are both negative

• They multiply to 10, not -10

• They add to -9, not -3

What is the correct factorization of the trinomial x^2 - 3x - 10?

• (x + 2)(x - 5)

• (x - 5)(x + 2)

• (x - 2)(x + 5)

• (x + 5)(x - 2)

What is the result of multiplying the binomials (x + 2)(x - 5)?

• x^2 - 3x - 10

• x^2 + 3x - 10

• x^2 - 7x + 10

• x^2 + 7x + 10

What is the significance of the middle term in factoring trinomials?

• It is always positive

• It is the product of the factors

• It determines the sign of the factors

• It is the sum of the factors

What does the final example in the video demonstrate?

• How to solve a quadratic equation

• How to factor a trinomial into binomials

• How to find the greatest common factor

• How to simplify a polynomial