Factoring Polynomials

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 out the GCF from a polynomial?

Back

To factor out the GCF, identify the largest factor common to all terms, then divide each term by the GCF and write it outside the parentheses.

Front

What is the first step in factoring the polynomial 8r^3 - 16r^2?

Back

Factor out the GCF, which is 8r^2, resulting in 8r^2(r - 2).

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a - b)(a + b).

Front

Factor the expression x^4 - 9x^2 completely.

Back

x^2(x + 3)(x - 3).

Front

What is the factored form of 14p^2 - 24p - 8?

Back

2(7p + 2)(p - 2).

Front

Identify one factor of the expression 4x^2 - 25.

Back

(2x - 5) is one of the factors.

Front

What is the factored form of 16q^3 - 48q^2 + 36q?

Back

4q(2q - 3)^2.

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means breaking it down into irreducible factors, where no further factoring is possible.

Front

What is the significance of factoring in solving polynomial equations?

Back

Factoring allows us to rewrite polynomial equations in a simpler form, making it easier to find roots or solutions.