Factoring

Front

What is the formula for the difference of cubes?

Back

The formula for the difference of cubes is: a³ - b³ = (a - b)(a² + ab + b²).

Front

Factor the expression: 8x³ - 28x² + 14x - 49.

Back

The factored form is: (4x² + 7)(2x - 7).

Front

Factor the expression: 12x³ + 16x² + 21x + 28.

Back

The factored form is: (4x² + 7)(3x + 4).

Front

What is the prime factorization of 120?

Back

The prime factorization of 120 is: 2³ × 3 × 5.

Front

What is the GCF of 10a²b³ and 20a²b²?

Back

The GCF is: 10a²b².

Front

What is the formula for the sum of cubes?

Back

The formula for the sum of cubes is: a³ + b³ = (a + b)(a² - ab + b²).

Front

How do you factor a quadratic expression of the form ax² + bx + c?

Back

To factor ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

Front

What is the difference between prime factorization and composite numbers?

Back

Prime factorization expresses a number as a product of its prime factors, while composite numbers are numbers that have more than two distinct positive divisors.

Front

What is the relationship between GCF and LCM?

Back

The relationship is given by: GCF(a, b) × LCM(a, b) = a × b.

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor out the common factor from each group, and then factor out the common binomial.