Factoring Polynomials

Front

What is factoring in mathematics?

Back

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

Front

What is the Greatest Common Factor (GCF)?

Back

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

Front

How do you factor the expression 3x^2 + 18x + 15?

Back

3(x + 5)(x + 1) is the factored form.

Front

What is the factored form of x^2 - 9x + 18?

Back

(x - 6)(x - 3) is the factored form.

Front

What method is used to factor the polynomial 5n³ - 10n² + 3n - 6?

Back

Factor by Grouping is the method used.

Front

What is the factored form of 4x^2 + 24x - 64?

Back

4(x + 8)(x - 2) is the factored form.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring technique used for expressions of the form a^2 - b^2, which factors into (a + b)(a - b).

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions, makes solving equations easier, and helps in graphing functions.

Front

How do you factor out the GCF from an expression?

Back

Identify the GCF of all terms, then divide each term by the GCF and write the expression as the GCF multiplied by the resulting expression.

Front

What is the factored form of 5ab^2c^11 + 2bc^5?

Back

bc^5(5abc^6 + 2) is the factored form.