Factoring Polynomials

Rewriting a polynomial as a product of polynomials of smaller degree is called _____ a polynomial.

• Factoring

• Distributive Property

• The Greatest Common Factor

Remember that you can apply the _____ to simplify expressions.

_____ - For all numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + ca

• Factoring

• Distributive Property

• The Greatest Common Factor

Example:
3(4x +5) = 3(4x) + 3(5) = 12x
Each term in the parentheses is multiplied by three to find the product. You can reverse the process to find the factors of the related product. The reverse process is called _____. You can factor polynomials to find the roots or solutions of an expression.

• Factoring

• Distributive Property

• The Greatest Common Factor

_____ is finding two or more factors of a number or a polynomial. To factor a monomial, find two or more expressions whose product is the given monomial.

• Factoring

• Distributive Property

• The Greatest Common Factor

_____ (_____) of two or more monomials is the common factor having the greatest numerical factor, with variables having the least degree. Thus, the term ax^n is the _____ of a polynomial if:
1. a is the greatest integer that divides each of the whole efficiency of the polynomials, and
2. n Is the smallest exponent of x in all the terms of the polynomial.

• Factoring

• Distributive Property

• The Greatest Common Factor

Given: 2x^2 - 4x^4
1. The greatest integer that is a factor of both 2 and 4 is _______.

Given: 2x^2 - 4x^4
2. The highest power of x present in both terms is

Given: 2x^2 - 4x^4
3. The GCF is

Given: 2x^2 - 4x^4
4. Dividing the first term by the GCF gives

Given: 2x^2 - 4x^4
5. Dividing the second term by the GCF gives