Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler 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 a polynomial completely?

Back

To factor a polynomial completely, identify and factor out the GCF, then look for patterns such as difference of squares, perfect square trinomials, or apply methods like grouping.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Tags

CCSS.HSA.APR.C.4

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² ± 2ab + b², which factors to (a ± b)².

Tags

CCSS.HSA.APR.C.4

Front

How do you factor the expression 5n³ - 10n² + 3n - 6?

Back

Factor by grouping: (5n² + 3)(n - 2).

Front

What is the factored form of 3x² + 18x + 15?

Back

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

Front

How do you factor the expression 81m² - 1?

Back

Use the difference of squares: (9m - 1)(9m + 1).

Tags

CCSS.HSA.APR.C.4

Front

What is the factored form of 25x² - 81?

Back

The factored form is (5x + 9)(5x - 9).

Tags

CCSS.HSA.APR.C.4

Front

How do you factor the expression x² + 9x - 36?

Back

Find two numbers that multiply to -36 and add to 9: (x + 12)(x - 3).