Factoring Polynomials

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 out the GCF from a polynomial?

Back

To factor out the GCF, identify the largest factor common to all terms, divide each term by the GCF, and write the polynomial as the product of the GCF and the resulting polynomial.

Front

What is the factored form of 8r³ - 16r²?

Back

4r²(2r - 4)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a + b)(a - b).

Front

Factor the expression x² - 36 completely.

Back

(x + 6)(x - 6)

Front

What is the Master Product method in factoring?

Back

The Master Product method involves finding two numbers that multiply to the product of the leading coefficient and the constant term, and add to the middle coefficient.

Front

What is the factored form of 5n³ - 10n² + 3n - 6?

Back

(5n² + 3)(n - 2)

Front

What is the first step in factoring by grouping?

Back

Group the terms in pairs and factor out the common factor from each pair.

Front

What is the factored form of n² + 16n + 63?

Back

(n + 7)(n + 9)

Front

How do you recognize a polynomial that can be factored by grouping?

Back

Look for a polynomial with four terms where pairs of terms share a common factor.