THE COMPOUND // FIELD NOTES // WEEK 05
Polynomials and value problems
Field Book
Lessons 16 to 19
Method
Paper first, every step
Multiplication of polynomials and the two workhorse word problem families: ratios and values.
What you have to be able to do
- Multiply polynomials by full distribution
- Work ratio problems with a multiplier table
- Write value equations for coin and ticket problems
The procedures
Multiply polynomialsField Book Lesson 16
- Distribute every term of the first parentheses through the second.
- Combine like terms at the end, and only at the end.
Subscripted variablesField Book Lesson 17
- Subscripts name different quantities. They change nothing about procedure.
- Treat P1 and P2 as two separate variables and solve as usual.
Ratio problemsField Book Lesson 18
- Build the table: given ratio, multiplier, actual amount.
- The same multiplier scales every row. Solve for it first.
Value problemsField Book Lesson 19
- Value equals number of items times value per item.
- Write one equation for counts and one for values, then solve the system.
Worked: a product of binomials
- Expand (x + 3)(x + 5).
- x times both terms, then 3 times both terms: x2 + 5x + 3x + 15.
- Combine: x2 + 8x + 15.
Terms on the record
| Term | Meaning |
|---|
| polynomial | a sum of terms with whole number exponents |
| subscripted variable | a variable named with a small index, such as P1 |
| value equation | number of items times value per item equals total value |