17_1-3-4 Homework Week 6
17.1 Homework
Example:
*The terms x^4, x^5, x^6, and x^7 have x^4 as the greatest common factor because the least exponent on the variable (x) in the factored forms is 4 :
x^4=1*x^4, x^
...
17_1-3-4 Homework Week 6
17.1 Homework
Example:
*The terms x^4, x^5, x^6, and x^7 have x^4 as the greatest common factor because the least exponent on the variable (x) in the factored forms is 4 :
x^4=1*x^4, x^5=x*x^4, x^6= x^2*x^4, x^7=x^3*x^4
GCF= x^4
** The exponent on a variable in the GCF is the least exponent that appears on that variable in ALL the terms, as shown above.
Steps to find
1. Factor - Write each number in their prime factoring form
2. List all common factors - List each prime number or each variable that is a factor of every term in the list.
3. Choose least exponents - Use as exponents on the common prime factors the least exponents from the now prime factored form.
4. Multiply – Multiply all the primes from Step 3.
*If there is no primes left after Step 3, the GCF is always 1.
Writing a polynomial (a sum) in factored form as a product is called factoring the polynomial.
For example, the polynomial : 3m+12 has 2 terms , 3m and 12. The GCF of these two terms is 3. Simply, the number 3 can factor into both the terms.
Ex: 3m+12
= 3 * m + 3 * 4
= 3 (m + 4)….. Which is the factored for of the polynomial example. This is called factoring out the Greatest Common Factor (GCF).
Factoring Trinomials
To Begin: We always want to remember the FOIL method when it comes to factoring trinomials.
( F- First // O- Outer ) // ( I- Inner // L- Last )
This method is used to check the binomials in the equation :
*Multiplying the Outer and Last products ADDED WITH Multiplying the First and
....................................................continued...........................................................
[Show More]
