AA-Factoring Polynomials

Front

What is the definition of factoring a polynomial?

Back

Factoring a polynomial involves rewriting it as a product of its factors, which are polynomials of lower degrees.

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF of a set of terms is the largest factor that divides each of the terms without leaving a remainder.

Front

Factor the polynomial completely: 2x^2 + 2x - 12

Back

2(x + 3)(x - 2)

Front

Factor the expression: x^2 - 1

Back

(x + 1)(x - 1)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states: a^2 - b^2 = (a + b)(a - b).

Front

Factor the expression: x^2 - 36

Back

(x + 6)(x - 6)

Front

How do you factor out the GCF from a polynomial?

Back

Identify the GCF of all terms, then divide each term by the GCF and write it outside the parentheses.

Front

What is the factored form of 2x^2 - 32?

Back

2(x - 4)(x + 4)

Front

What is the formula for factoring a trinomial of the form ax^2 + bx + c?

Back

To factor, find two numbers that multiply to ac and add to b, then rewrite the middle term.

Front

Factor the polynomial: 24x^9 - 36x^6 + 60x^3

Back

6x^3(4x^6 - 6x^3 + 10) or 6x^3(4x^3 - 6 + 10/x^3) depending on further simplification.