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!
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Algebra 1a: Chapter 7, Lesson 8, page 338
Parallel and Perpendicular Lines
Parallel lines by definition have the same slope. So, for the equation of 2 lines, all we have to do is figure out what the slope is of them both. If they have the same slope, then they are parallel. Check too, however, to make sure that both lines have DIFFERENT y-intercepts. If they have the same slope and y-intercept, then they are the same line, one on top of the other.
Perpendicular lines are lines that intersect at 90° or are at right angles to each other. By definition, the slopes of 2 lines that are perpendicular, when multiplied together, have a resultant product of −1.
Remember, the slope-intercept formula to find the slope, `m`: `y = mx + b`
You MAY have to solve the equation lines for `y`, isolating it to see what the slope, `m`, is as well as the y-intercept, `b`.
Here is a link from purplemath too with more explanation and examples.
Two of tonight’s homework problems solved by MrE are here! Just click it!