THE COMPOUND // FIELD NOTES // WEEK 07
Fractional equations, GCF, and factoring
Field Book
Lessons 24 to 27
Due
Test 5 due ยท Supplement 7
Method
Paper first, every step
Factoring opens for business. The trinomial pattern learned this week carries half the year.
What you have to be able to do
- Clear fractions from an equation with the LCD
- Pull the greatest common factor in two steps
- Factor trinomials and add rational expressions
The procedures
Fractional equationsField Book Lesson 24
- Multiply every term by the LCD to clear all fractions.
- Solve the cleared equation, then check the answer against the original denominators.
Greatest common factorField Book Lesson 25
- Find the GCF in two steps: numbers first, then variables.
- Write the GCF outside and the leftover factors inside the parentheses.
Trinomial factoringField Book Lesson 26
- For x2 + bx + c, hunt two numbers that multiply to c and add to b.
- Write the two binomials and multiply back to confirm.
Adding rational expressionsField Book Lesson 27
- Build each fraction to the LCD by asking what is missing from its denominator.
- Multiply top and bottom by the missing factor, then add the numerators.
Worked: a trinomial
- Factor x2 + 7x + 12.
- Two numbers that multiply to 12 and add to 7: 3 and 4.
- x2 + 7x + 12 = (x + 3)(x + 4).
Terms on the record
| Term | Meaning |
|---|
| greatest common factor | the largest expression that divides every term |
| trinomial | a polynomial with exactly three terms |
| rational expression | a fraction whose top and bottom are polynomials |