Algebra: Chapter 10, Lesson 9, page 465.
Dividing Polynomials
To divide a polynomial by a monomial, divide each term by that monomial.
For example:
`(6x^2 + 3x – 2)/3` becomes `(6x^2)/3 + (3x)/3 -2/3` or simplifying terms, we have
`2x^2 + x – 2/3`
If the divisor is not a monomial, then we need to use long (I call it synthetic from my ‘oldness’) division. It is just like regular division but takes a little getting use to.
A tip is that the quotient should be in descending order and you need to include the missing terms by sticking in ZEROES.
If the quotient is `x^3-x+1`, I would re-write it as `x^3+0x^2+0x^1+1`. Practice makes perfect. Examples 3, 4 and 5 on pages 465 and 466 are pretty easy to follow.
Here is a link from purplemath.com for more clarification.
Two of tonight’s homework problems solved by MrE are here! Just click it
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Algebra 1a: Chapter 8, Lesson 5, page 380.
Motion Problems
D-R-T Problems (otherwise known as DIRT problems). `D` is the distance, `R` is the rate (or speed like miles per hour [mph] or kilometers per hour [kph] or feet per second [ft/sec]) and `T` is the time. Be careful and make sure that if the rate is in mph, then the time has to be in hours. If the rate is in feet/sec, then the time has to match and be in seconds as well.
For those type of problems that have 2 people starting off, remember that the first person’s time is `t`, but the second person (who leaves later) actually has `t – x` time where x is the time delay of the second person leaving. For example if one person leaves at `t` and the second leaves 2 hours later, then the second person’s time is `t – 2`.
REMEMBER, diagrams are great to get you to understand what you are looking for. The tables in the book are also good techniques. The more pictures or diagrams you have, the better chance you have of understanding what steps you have to go through! GO SLOW!!
Here are some links to excellent D-R-T examples at the PurpleMath website. Its easier to link to these than show you the same thing!
Two of tonight’s homework problems solved by MrE are here! Just click it!