Short post today and some accurate/creative responses may earn reduced homework.
Question 1 - What is a depressed polynomial? (in your own words)
Question 2 - Why did the polynomial choose to be become depressed? (joke responses/ meaning based responses glady accepted)
A depressed polynomial is the resulting quotient that you get when you divide a polynomial by a binomial. For example, if you divided ((x^2)-2x-8) by (x+2), the quotient, or answer, would be (x-4). Therefore, (x-4) is the depressed polynomial.
ReplyDeleteImpressive...For being the first poster, you can depress your HW 7.3 by 5 problems. (Just not the more difficult problems at the end).
Delete1) When you divide a polynomial [by a binomial], the resulting [binomial] factor is the depressed polynomial (i.e. x^2 + 5x + 6 divided by x + 3 would give you x + 2, the depressed polynomial).
ReplyDelete2) The polynomial once had two, solid binomial factors, which made it very happy. Then, one day, an insidious mathematician decided to split the polynomial up, and took away one of its precious factors, leaving it with just one teensy little binomial. Thus, the once proud polynomial was left depressed.
By the way, I put binomial in brackets above because I'm a little unsure--does the polynomial HAVE to be divided by a binomial/become a binomial to be considered depressed? For example, would it be wrong to say that 12x^3 + 5x^2 + 8x + 4 divided by x^2 + 2x + 5 would result in a depressed polynomial (horrible example, I know)?
- Lily