Factoring Trinomials: Techniques and Strategies

In this video, Mr. Banker explains how to factor trinomials by combining different factoring techniques. He demonstrates factoring using the greatest common factor (GCF) and sum and product methods through examples. The video also highlights that not all trinomials are factorable and emphasizes the importance of verifying the results by refoiling the binomials.

What is the first step in factoring any polynomial?

• Identify the highest exponent

• Find the greatest common factor

• List all possible factors

• Determine the coefficients

What does factoring out the GCF from a trinomial involve?

• Adding the GCF to each term

• Subtracting the GCF from each term

• Dividing each term by the GCF

• Multiplying the common factor

Which pair of numbers adds up to 3 and multiplies to 18?

• 6 and 3

• 3 and 6

• 2 and 9

• 1 and 18

After factoring out the GCF, what is the next step in factoring a trinomial?

• Combine like terms

• Apply the quadratic formula

• Graph the equation

• Use the sum and product method to find factors

What is the result of factoring 3x^2 - 6x - 72?

• 3(x - 4)(x + 6)

• 3(x + 4)(x - 6)

• 3(x - 6)(x + 4)

• 3(x + 6)(x - 4)

Which numbers need to add up to -2 and multiply to 24?

• 2 and 12

• 4 and 6

• 3 and 8

• 1 and 24

What indicates that a trinomial cannot be factored using standard methods?

• The GCF is 1

• The trinomial is not set to zero

• No pair of factors can be found that meet the necessary conditions

• It has a prime number as a coefficient

What should you do if the factors found do not reproduce the original trinomial when foiled?

• None of the above

• Multiply the factors

• The trinomial is prime

• Revise the factors

What is the correct factored form of the trinomial x^2 + 8x + 33?

• (x + 3)(x + 11)

• Not factorable

• (x - 11)(x + 3)

• (x + 11)(x - 3)

Why is it important to refoil the binomials obtained from factoring?

• To verify the accuracy of the factoring

• To simplify the expression further

• To determine the roots of the polynomial

• To find the GCF