Factoring Trinomials: x² + bx + c

What is the first step in factoring a trinomial using the FOIL method?

• Identify the middle term

• Multiply the first terms of each binomial

• Add the products of the outer and inner terms

• Determine the constant term

Which pair of numbers multiplies to 15 and adds up to 8?

• 3 and 5

• 1 and 15

• 2 and 7

• 4 and 11

What is the product of the constants in the binomials that factor x^2 + 10x + 21?

• 21

• 10

• 31

• 11

Which of the following is a correct factorization of x^2 + 8x + 15?

• x + 5 and x + 3

• x - 5 and x - 3

• x + 3 and x + 5

• x - 3 and x - 5

What is the factored form of x^2 + 7x + 12?

• x + 3 and x + 4

• x + 4 and x + 3

• x - 3 and x - 4

• x - 4 and x - 3

How do you determine the signs of the factors in a trinomial with a positive constant term?

• Both signs are negative

• Both signs are positive

• One sign is positive, the other is negative

• Cannot determine from the constant term alone

For the trinomial x^2 - 6x + 8, what are the correct factors?

• x + 4 and x + 2

• x - 2 and x - 4

• x + 2 and x + 4

• x - 4 and x - 2

How do you factor a trinomial with a negative constant term?

• Use only positive factors

• It cannot be factored

• Use only negative factors

• Use one positive and one negative factor

In a rectangle area problem, if the trinomial is x^2 - 2x + 35, what could be the dimensions of the rectangle?

• x - 7 and x + 5

• x - 5 and x + 7

• x + 5 and x - 7

• x + 7 and x - 5

What is the factored form of a trinomial with multiple variables, given the trinomial x^2 - 5xy + 6y^2?

• (x + 3y)(x + 2y)

• (x - 3y)(x - 2y)

• (x + 2y)(x + 3y)

• (x - 2y)(x - 3y)