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prime number, which is 2. We get 36. We can then divide 36 by 2 to get 18. We continue dividing by prime numbers until we get all prime factors: 2 x 2 x 2 x 3 x 3 = 72.

• Factor 4x^2 – 12x + 9.

We can start by factoring out the greatest common factor, which is 1: (2x – 3)^2. Then, we can see that the expression is a perfect square trinomial and write it as (2x – 3)(2x – 3).

• Find the GCF of 42 and 70.

To find the GCF of 42 and 70, we can list the factors of each number: 42: 1, 2, 3, 6, 7, 14, 21, 42; 70: 1, 2, 5, 7, 10, 14, 35, 70. The largest number that appears in both lists is 14, so the GCF of 42 and 70 is 14.

• Factor x^3 – 8.

We can use the difference of cubes formula to factor this expression: (x – 2)(x^2 + 2x + 4).

FAQ:

• What is the difference between a prime factor and a composite factor?

A prime factor is a factor that is a prime number, while a composite factor is a factor that is not a prime number. A composite number has more than two factors.

• Why is finding factors important in mathematics?

Finding factors is important in mathematics because it can help simplify expressions, solve equations, and identify patterns in data. It is used in many areas of mathematics, including algebra, geometry, and number theory.

• What is the greatest common factor?

The greatest common factor is the largest factor that two or more numbers have in common. It is often used to simplify expressions and solve equations.

• How do you factor a quadratic expression?

To factor a quadratic expression, you need to find two numbers that multiply to the constant term and add to the coefficient of the x-term. You can then write the expression as the product of two binomials.

• What is factoring?

Factoring is the process of finding the factors of a number or an algebraic expression. It is used to simplify expressions, solve equations, and identify patterns in data.

Quiz:

1. What are factors? A) Numbers or algebraic expressions that are multiplied by other numbers or expressions B) Numbers or algebraic expressions that are divided by other numbers or expressions C) Numbers or algebraic expressions that are added to other numbers or expressions D) Numbers or algebraic expressions that are subtracted from other numbers or expressions
2. What is a prime factor? A) A factor that is a prime number B) A factor that is not a prime number C) A factor that is both a prime number and a composite number D) A factor that is negative
3. What is the greatest common factor? A) The smallest factor that two or more numbers have in common B) The largest factor that two or more numbers have in common C) The smallest factor of a single number D) The largest factor of a single number
4. How do you factor a quadratic expression? A) By dividing by the constant term B) By finding two numbers that add to the coefficient of the x-term C) By finding two numbers that multiply to the coefficient of the x-term and add to the constant term D) By multiplying the x-term by the
5. What is the difference between factoring and expanding? A) Factoring is the process of writing an expression as the product of two or more factors, while expanding is the process of multiplying out an expression. B) Factoring is the process of multiplying out an expression, while expanding is the process of writing an expression as the product of two or more factors. C) Factoring and expanding are the same process. D) Factoring is used for addition and expanding is used for subtraction.
6. What is the factor tree method? A) A method for finding the greatest common factor of two or more numbers B) A method for finding the prime factorization of a number C) A method for simplifying algebraic expressions D) A method for solving quadratic equations
7. What is the prime factorization of 60? A) 2 x 3 x 5 B) 2 x 2 x 3 x 5 C) 3 x 5 x 7 D) 2 x 2 x 5 x 5
8. What is the factorization of x^2 – 4? A) (x – 2)(x – 2) B) (x + 2)(x + 2) C) (x – 2)(x + 2) D) (x – 4)(x + 4)
9. What is the GCF of 12x^2 and 18x? A) 6x B) 12x C) 18x D) 24x^2
10. What is the factorization of 2x^2 – 10x + 12? A) 2(x – 2)(x – 3) B) 2(x – 2)(x + 3) C) (x – 2)(x – 3) D) (x – 2)(x + 3)

    Answers:

    1. A
    2. A
    3. B
    4. C
    5. A
    6. B
    7. B
    8. C
    9. 6x
    10. 2(x – 2)(x – 3)

    In conclusion, factoring is an essential tool in mathematics that can help simplify expressions, solve equations, and identify patterns in data. Understanding factors and factorization can help students excel in algebra, geometry, and number theory. By practicing the examples and taking the quiz, students can reinforce their understanding of factors and factorization and become more confident in their mathematical abilities.