Factoring Trinomials: GCF and Prime Techniques

What does it mean if a trinomial is identified as prime?

• It can be factored into two binomials.

• It can be simplified to a monomial.

• It cannot be factored.

• It has a Greatest Common Factor other than 1.

What is the first step in factoring trinomials?

• Determine if the trinomial is prime.

• Apply the quadratic formula.

• Identify the GCF.

• List all possible factors.

How do you determine the correct factors of 14 that sum up to -9C?

• 1 and 14

• 2 and 7

• -2 and -7

• None of the above

What is the significance of taking out a GCF of -1 in factoring trinomials?

• It simplifies the trinomial to its prime factors.

• It ensures all terms are positive.

• It reverses the signs of all terms in the trinomial.

• It has no effect on the factoring process.

Which factors of 24 add up to 14R when factoring trinomials?

• 6 and 4

• 3 and 8

• 2 and 12

• 1 and 24

Why is a trinomial considered prime if no factors can be found that sum up to its middle term?

• Because it can still be factored using complex numbers.

• Because it indicates a mistake in the initial problem.

• Because it can be simplified further.

• Because it cannot be factored into binomials.

What does factoring out a GCF from a trinomial accomplish?

• It makes the trinomial easier to factor further.

• It has no significant effect on the trinomial.

• It changes the trinomial into a binomial.

• It simplifies the trinomial to a prime number.

In the example with variables Z, what was the GCF taken out?

• 10Z

• 2Z

• Z^2

• 18

How do you determine the correct factors that sum up to 10A in the last example?

• -2 and 12

• 3 and 8

• 2 and -12

• 1 and 24

What is the final step in factoring a trinomial after finding the correct factors?

• Multiply the factors to check the original trinomial.

• Divide the trinomial by the GCF.

• Add the GCF back to the factored form.

• Simplify the trinomial further.