Factoring ALL methods

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together give the original expression.

Front

What is the purpose of factoring by grouping?

Back

Factoring by grouping is used to factor polynomials that have four or more terms by grouping terms in pairs and factoring out the common factors.

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or terms without leaving a remainder.

Front

How do you factor a quadratic expression of the form ax^2 + bx + c?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the expression using these numbers.

Front

What is the difference between prime and composite polynomials?

Back

A prime polynomial cannot be factored into simpler polynomials with integer coefficients, while a composite polynomial can be factored into two or more non-trivial polynomials.

Front

Factor the expression: 5n³ - 10n² + 3n - 6.

Back

(5n² + 3)(n - 2) using factoring by grouping.

Front

Factor the expression: 3x² + 5x - 12.

Back

(x + 3)(3x - 4) by finding two numbers that multiply to -36 and add to 5.

Front

What is the first step in factoring 3x² + 18x + 15?

Back

The first step is to factor out the GCF, which is 3, resulting in 3(x² + 6x + 5).

Front

Factor the expression: x² + 7x + 12.

Back

(x + 3)(x + 4) by finding two numbers that multiply to 12 and add to 7.

Front

Factor the expression: k² - 2k - 24.

Back

(k + 4)(k - 6) by finding two numbers that multiply to -24 and add to -2.