Factoring Trinomials with a=1

What is the primary goal when factoring trinomials in the form x^2 + bx + c?

• To find two numbers that multiply to c and add to b

• To find two numbers that multiply to b and add to c

• To subtract the constant term from the middle term

• To divide the trinomial into multiple binomials

In the area model, if the product is x^2 + 7x + 12, which pair of factors of 12 add up to 7?

• 2 and 6

• 3 and 4

• 6 and 2

• 1 and 12

Which pair of factors of 12, when used in the area model, results in a trinomial of x^2 + 13x + 12?

• 2 and 6

• 3 and 10

• 1 and 12

• 6 and 7

How can negative factors be used in the area model to achieve a positive constant term?

• Multiply two negative factors

• Add two negative factors

• None of the above

• Subtract two negative factors

In the case of a trinomial with a leading coefficient of 1, how do you determine the binomial factors?

• By multiplying the constant term by the middle term coefficient

• By finding two factors of the constant term that add to the middle term coefficient

• By finding any two factors of the constant term

• By dividing the constant term by the middle term coefficient

What is the greatest common factor (GCF) used for in the context of factoring trinomials?

• To determine the coefficients of the binomials

• To adjust the signs of the factors

• To find the factors of the constant term

• To simplify the trinomial before factoring

If the sum needed is 8 and the product is 12, which pair of factors of 12 would be suitable?

• 4 and 8

• 2 and 6

• 1 and 7

• 3 and 5

What does a negative product in the area model indicate about the factors?

• The factors are zero

• One factor is positive and one is negative

• Both factors are negative

• Both factors are positive

When factoring trinomials, why is it important to consider the greatest common factor first?

• It simplifies the trinomial making the factoring process easier

• It changes the signs of the factors

• It increases the value of the constant term

• It has no impact on the factoring process

What is the correct set of binomial factors for the trinomial x^2 + 3x + 2?

• x - 2 and x - 1

• x + 2 and x + 1

• x - 1 and x - 2

• x + 1 and x + 2