Page 253 - Algebra 1

Example
2
Determining the GCF of Algebraic Expressions
Find the GCF of each expression.
a. 6a2b3 + 8a2b2c
SOLUTION
Write the prime factorization for both terms.
6a2b3 =2·3·a·a·b·b·b 8a2b2c=2·2·2·a·a·b·b·c
Find all factors that are common to both terms. 6a2b3 =2·3·a·a·b·b·b
8a2b2c = 2 · 2 · 2 · a · a · b · b · c
Each term has one factor of 2, two factors of a and two factors of b, so the
GCFof 6a2b3 and8a2b2cis2·a·a·b·b=2a2b2.
b. 8c4d2e - 12c3d4e2 SOLUTION
8c4d2e = 2 · 2 · 2 · c · c · c · c · d · d · e 12c3d4e2 =2·2·3·c·c·c·d·d·d·d·e·e The GCF is 4c3d2e.
Finding the GCF of a polynomial allows you to factor it and to write the polynomial as a product of factors instead of the sum or difference of monomials.
Factoring a polynomial is the inverse of the Distributive Property. Using the Distributive Property will “undo” the factoring of the GCF.
Factoring a Polynomial
Factor each polynomial completely.
a. 6x3 +8x2 -2x
SOLUTION
Find the GCF of the terms. The GCF is 2x.
Write each term of the polynomial with the GCF as a factor. 6x3 +8x2 -2x=2x·3x2 +2x·4x-2x·1
2x(3x2 + 4x - 1)
Check
2x(3x2 +4x-1)
2x (3x2) + 2x(4x) - 2x(1) Use the Distributive Property.
6x3 + 8x2 - 2x Multiply each term by the GCF. The factored polynomial is the same as the original polynomial.
Example
3
Hint
You can also divide
each term by the GCF.
_6x3 =3x2 2x
238 Saxon Algebra 1