Factoring and Prime Factorization Concepts

The video tutorial explains how to factor a trinomial by identifying and using the greatest common factor (GCF). It begins with determining the prime factorization of each term in the trinomial, then identifies the GCF by finding common factors. The tutorial demonstrates factoring the trinomial by factoring out the GCF and verifies the result by multiplying the factors to ensure the original trinomial is obtained.

What is the first step in factoring a trinomial by its greatest common factor?

• Divide each term by the smallest number

• Add all the terms together

• Find the prime factorization of each term

• Determine the coefficients

What is the prime factorization of 30?

• 3 x 5 x 6

• 2 x 5 x 6

• 3 x 3 x 5

• 2 x 3 x 5

Which of the following is a prime factor of 36?

• 4

• 6

• 2

• 9

What is the prime factorization of 12?

• 2 x 2 x 3

• 3 x 4

• 3 x 3

• 2 x 6

What is the greatest common factor of the terms 30x^3, 36x^2, and 12x?

• 2x

• 12x

• 6x

• 3x

What is left when you factor 6x out of 30x^3?

• 6x^2

• 6x

• 5x

• 5x^2

After factoring 6x from 36x^2, what remains?

• 2x^2

• 6x

• 6

• 2x

What is the result of factoring 6x from 12x?

• 6

• 2

• 1

• 12

What is the factored form of the trinomial 30x^3 - 36x^2 + 12x?

• 6x(5x^2 + 6x - 2)

• 6x(5x^2 - 6x - 2)

• 6x(5x^2 + 6x + 2)

• 6x(5x^2 - 6x + 2)

How do you verify the factored form of a trinomial?

• By subtracting the factors

• By multiplying the factors

• By dividing the factors

• By adding the factors