Algebra: Chapter 5, Lesson 8, page 236.
Subtraction of Polynomials
We do just like the addition of polynomials, except for subtraction, we (remember way back to subtracting with negative numbers) add the opposite. The other thing we have to remember is the sign problems for double negatives, make “Change-change” or “bling-bling” with 2 negatives.
You can do the subtraction horizontally or vertically. Horizontally requires that you scan across the polynomials. It’s easier for me to put the polynomials in descending order and then combine like terms, remembering the combining terms MUST HAVE THE SAME VARIABLE AND THE SAME EXPONENTS!
If you do the problems horizontally, remember that the `-` sign turns everything in 2nd polynomial’s parenthesis `( x^2 …)` to its opposite sign!
Vertically (or columns in the textbook) require you to write out the problem with spaces for missing terms. It is easier to line up terms this way and you can stick in other terms as well that are not common to both polynomials.
See here for more examples too.
Two of tonight’s homework problems solved by MrE are here! Just click it!
======================================================================
Algebra 1a: Chapter 4, Lesson 5, page 187.
Using Inequalities
We learned key phrases for lesson 5 (word translation problems):
- “Less than or equal to”, “is at most”, “no more than” — ≤
- “No less than”, “at least”, “more than or equal to” — ≥
- “Is less than” — <
- “Is greater than” — >
We learned to read the problem, draw a picture or understand what is being asked of us before we start solving an equation or inequality.
Remember for 2 step inequalities, we do the same, again, as equalities and solve by:
- Distributing when required
- Combining like terms
- Adding or subtracting terms to isolate variables and numbers (constants)
- Multiplying or dividing to finish solving for the variable, remembering to reverse the sign of the inequality IF we multiply or divide by a NEGATIVE NUMBER.
Here are some keyword descriptions from purplemath.com to help us with word problems (ugh …)
Two of tonight’s Lesson 5 homework problems solved by MrE are here! Just click it!