Factoring Trinomials Day #2

You are trying to factor x² + x - 56. At left are some combination of factors that multiply to -56. What pair might you try first?

• 1, -56

• -4, 14

• 7, -8

• -7, 8

Let that sink in, the pair of factors you would use to factor

x² + x - 56

would be 7 and -8. Why do you think that is?

Evaluate responses using AI:

OFF

Which of the following would be the factored form of;

x² + x - 56?

• (x - 7)(x + 8)

• (x + 8)(x + 7)

• (x - 8)(x + 7)

• None of these are the correct factored form.

Okay, how about this one? Which of the following would be the factored form of

x² + 26x - 56?

• (x + 28)(x - 2)

• (x + 28)(x + 2)

• (x - 28)(x +2)

• (x - 28)(x -2)

One more... Which of the following would be the factored form of

x² - 10x - 56?

• (x + 14)(x - 4)

• (x + 14)(x + 4)

• (x - 14)(x + 4)

• (x - 14)(x - 4)

x² + x - 56 = (x - 7)(x + 8)

x² + 26x - 56 = (x + 28)(x - 2)

x² - 10x - 56 = (x - 14)(x + 4)

These were the factored forms of the quadratic trinomials. Which of the following BEST describes the relationship between the constant and the middle term. The factors ___. Select all that apply

• MULTIPLY to give the constant

• ADD to give the middle term

• MULTIPLY to give the middle term

• ADD to give the constant

Let's work with that idea a little bit more. Use the figure on your sheet to find the middle term.

x² + ____ - 40

• 6x

• 10x

• 4x

• -14x

Use the box on the handout to complete;

___² + 20x + ___

Use the box on the handout to complete the factoring of;

x² - 3x - 10

• (x - 5)(x + 2)

• (x + 5)(x - 2)

• (x - 5)(x - 2)

• None of these are the correct factoring

• (x - 4)(x + 5)

• (x + 4)(x + 5)

• (x + 1)(x + 20)

• (x + 2)(x + 10)