Factoring Trinomials Using the Diamond Method

This video tutorial covers factoring trinomials using the diamond method. It begins with an introduction to the method and proceeds with examples where the leading coefficient a is 1 and where a is not 1, explaining the additional steps required in the latter case. The importance of checking for a greatest common factor (GCF) before factoring is emphasized. The tutorial concludes with a complex example involving fractions, demonstrating the complete factoring process.

What are the two numbers that multiply to 24 and add up to -14?

• -12 and -2

• -2 and 2

• -12 and 12

• 12 and 2

What is the factored form of the polynomial x^2 - 14x + 24?

• (x-2)(x+2)

• (x-12)(x-2)

• (x+12)(x+2)

• (x-12)(x+12)

Which pair of numbers multiplies to -15 and adds up to 2?

• 5 and 3

• -3 and -5

• 3 and -5

• 5 and -3

How do you verify the factored form of a trinomial?

• By using the FOIL method

• By adding

• By dividing

• By subtracting

What additional step is needed when 'a' is not 1 in factoring trinomials?

• Multiply by 'a'

• Divide by 'a'

• Subtract 'a'

• Add 'a'

What is the factored form of 3x^2 + 11x + 6?

• 3(x+3)(x+2)

• 3(x-3)(x-2)

• (3x+2)(x+3)

• (3x+3)(x+2)

What should you always check before factoring a polynomial?

• If it can be simplified

• For a GCF

• If it is prime

• For a LCM

What is the result of factoring the polynomial y^2 - 4y - 5 after factoring out a GCF of 9?

• 9(y+1)(y-5)

• 9(y+5)(y-1)

• 9(y-5)(y+1)

• 9(y-1)(y+5)

What is the correct factored form of the polynomial 4x^2 + 4x - 12?

• (4x+6)(x-2)

• 2(x+1.5)(x-0.5)

• 4(x+3)(x-1)

• 2(x+3)(x-1)

How do you handle non-integer results when factoring with a coefficient not equal to 1?

• Ignore the fractions

• Move the denominator to the front

• Only use whole numbers

• Round to the nearest whole number