Factoring - Math Notes
Common Factoring: Find out the GREATEST COMMON FACTOR of each term and factor it out.
Using Grouping:
Sometimes, a polynomial will have no common factor for all the terms. Instead, we can group together the terms which have a common factor.
When you use the Grouping Method: * When there is no factor common to all terms * When there is an even number of terms.
Example:
The polynomial x3+3x2−6x−18 has no single factor that is common to every term. However, we notice that if we group together the first two terms and the second two terms, we see that each resulting binomial has a particular factor common to both terms.
Factor x2 out of the first two terms, and factor −6 out of the second two terms. x2(x+3) −6(x+3)
Now look closely at this binomial. Each of the two terms contains the factor (x+3).
Factor out (x+3).
(x+3) (x2−6) is the final factorization. x3+3x2−6x−18= (x+3) (x2−6)
Factoring Trinomials:
Notice that the first term in the resulting trinomial comes from the product of the first terms in the binomials: x⋅x=x2. The last term in the trinomial comes from the product of the last terms in the binomials: 4⋅7=28. The middle term comes from the addition of the outer and inner products: 7x+4x=11x. Also, notice that the coefficient of the middle term is exactly the sum of the last terms in the binomials: 4+7=11.
Method of Factoring 1. Write two sets of parentheses:( ) ( ). 2. Place a binomial into each set of parentheses. The first term of each binomial is a factor of the first term of the trinomial. 3. Determine the second terms of the binomials by determining the factors of the third term that when added together yield the coefficient of the middle term.
*inquire about guess and check method
Difference of Squares Equation:
Using Grouping:
Sometimes, a polynomial will have no common factor for all the terms. Instead, we can group together the terms which have a common factor.
When you use the Grouping Method: * When there is no factor common to all terms * When there is an even number of terms.
Example:
The polynomial x3+3x2−6x−18 has no single factor that is common to every term. However, we notice that if we group together the first two terms and the second two terms, we see that each resulting binomial has a particular factor common to both terms.
Factor x2 out of the first two terms, and factor −6 out of the second two terms. x2(x+3) −6(x+3)
Now look closely at this binomial. Each of the two terms contains the factor (x+3).
Factor out (x+3).
(x+3) (x2−6) is the final factorization. x3+3x2−6x−18= (x+3) (x2−6)
Factoring Trinomials:
Notice that the first term in the resulting trinomial comes from the product of the first terms in the binomials: x⋅x=x2. The last term in the trinomial comes from the product of the last terms in the binomials: 4⋅7=28. The middle term comes from the addition of the outer and inner products: 7x+4x=11x. Also, notice that the coefficient of the middle term is exactly the sum of the last terms in the binomials: 4+7=11.
Method of Factoring 1. Write two sets of parentheses:( ) ( ). 2. Place a binomial into each set of parentheses. The first term of each binomial is a factor of the first term of the trinomial. 3. Determine the second terms of the binomials by determining the factors of the third term that when added together yield the coefficient of the middle term.
*inquire about guess and check method
Difference of Squares Equation: