Factoring in Algebra

1. Factoring in Algebra

2. Throughout math, you will use a process known as factoring in many different problems.  It is used when solving polynomial equations, to simplify things, and many other purposes.

3. The Process of Factoring

4. Using the distributive property lets us change an expression from a product to a sum.  For example, an expression such as 3a(x-c) tells you to multiply3aby x-c.  When you do that, you get the sum 3ax -3ac.  When you do that in reverse, by writing 3ax - 3ac as the product of the two factors3a and x-c, you are factoring.

5. Example: • 1. Factor:4a^3b^4z^3+2a^2bz^4 Solution:Write out the terms as products of their prime and literal factors. 2*2*a*a*a*b*b*b*b*z*z*z + 2*a*a*b*z*z*z*z Each term has at least one 2, two a's, one b, and three z's as factors. Therefore, theGCF is2a^2bz^3.

6. Now that you've got the GCF factored out, you can rewrite the two terms without the factors in the GCF. 2 * a * b * b * b + z The second pair of parentheses can now be filled in with the rewritten terms. (2a^2bz^3)(2ab^3+z)is the answer. (2a^2bz^3)( )

7. Factoring Trinomials

8. Using a multiplication problem consisting of two binomials, we will show some important things to remember when factoring trinomials, which is the reverse of multiplying two binomials.

9. 1.The first term of the trinomial is the product of the first terms of the binomials. 2.The last term of the trinomial is the product of the last terms of the binomials. 3.The coefficient of the middle term of the trinomial is the sum of the last terms of the binomials.

10. 4.If all the signs in the trinomial are positive, all signs in both binomials are positive. 5.Keeping these important things in mind, you can factor trinomials.