ANSWER CHOICES:
A. binomial
B. trinomial
C. 2
D. 3
E. 4
F. x2 - 4x - 4
G. 42x2 - 23x + 17
H. x2 + 7x + 12
I. 10x2 - 50x + 60
J. 2x2 + 5x - 12
K. -2x2 + 6x - 4
L. 3x + 2 + 5/(x + 1)
M. 3x2 - 4x + 2
N. x2 + 6x + 9
O. x2 - 6x + 9
P. 2x + 5
Q. -2x3 - 11x2 + 3
R. 2x3 + x2 - 6x + 27
S. x2 - 16
T. 18x2 - 11x - 24
U. x2 + 8x + 16
V. x2 - 4
W. x2 - 9
X. x2 - 8x + 27 + [-96/(x + 3)]
Y. 9x2 - 4
Z. 14x + 25

Question 11
(x4 + 4) is what type of polynomial?

Question 12
(10x + 15) + (4x + 10) =

Question 13
(1 - 2x)(x2 + 6x + 3) =

Question 14
(x - 3)(10x - 20) =

Question 15
Subtract (-16x2 - 19x - 10) from (-18x2 - 13x - 14)

Question 16
(x + 4)2 =

Question 17
The polynomial (6x3 + 13x2 - 29x + has how many terms?

Question 18
(3x2 + 5x + 7) / (x + 1)

Question 19
(3x - 2)(3x + 2)=

Question 20
For a square with side of length (x + 3), it's area is square units.

I find Greek much more challenging than these problems. I'll try to explain how to approach them in a way that involves hopefully not thinking too much.

For 11 the answer must be either A or B: only these could conceivably describe a "type of polynomial." If you look in a textbook or on the web you find that "binomial" means "polynomial with two terms" and "trinomial" means "polynomial with three terms." x^4 + 4 has only two terms in it, x^4, and 4, it is a binomial, so A.

[I should say that without a list of answers given, I would have no idea how to answer this, since there are all sorts of ways to describe polynomials. If you stopped a random person with a math degree on the street and asked them what kind of polynomial x^4 + 4 was they would probably use some other description. e.g. because the highest power appearing in it is 4, many would say "it is a polynomial of degree 4," which is certainly true, but not one of the options.]

In 12 there is no substitute for just adding these together. This is done by adding like terms. You add 10x and 4x together to get 14x and 15 and 10 together to get 25, so 14x + 25, so Z. (Even without doing the addition you can rule most of the possible answers out right away because they involve higher powers of x, like x^2, in them. Adding polynomials involving only x and numbers together can never lead to higher powers of x.)

In 13 you can just multiply it out.

(1 - 2x)(x^2 + 6x + 3) = 1 (x^2 + 6x + 3) - 2x (x^2 + 6x + 3)
= x^2 + 6x + 3 - 2x(x^2) - 2x(6x) - 2x(3)
= x^2 + 6x + 3 - 2x^3 - 12x^2 - 6x
now collect like terms:
= -2x^3 + (x^2 - 12x^2) + (6x - 6x) + 3
and simplify:
= -2x^3 - 11x^2 + 3 so Q.

If you know about the "leading term" of a polynomial (= the term involving the highest power of x) you could have actually skipped the calculation. Whatever the product is, its leading term will be the product of the leading terms of 1 - 2x and x^2 + 6x + 3, namely, the product (-2x)(x^2) = -2x^3. Q is the only polynomial listed with this as its leading term.

For the same reason 14 has to be I since the leading term of the product will be x*(10x) = 10x^2, and only one option on the list has this as its leading term. But to doublecheck you should multiply those polynomials out and see that I really does give you the product.

In 15, the leading term of the difference will be (-18 x^2) - (-16 x^2) = (-18 + 16) x^2 = -2x^2 and only K has -2x^2 as its leading term, so it's K. But to doublecheck you should actually subtract the polynomials. For example the x term in the difference will be -13x - (-19)x = (-13 + 19) x = 6x which checks out with K also and you should also check the constant term.

In 16, just compute the product, (x + 4)(x + 4). It turns out to be U.

In 17, four. To do this you just need to know that each of 6x^3, 13x^2, -29x, 8 is a term. (Even without knowing what "term" means, you see the answer must be one of CDE since only these are numbers.)

In 18 you should actually perform the division. It is complicated to describe so hopefully you have a book that contains some examples. It turns out to be L, although you could almost guess this from other reasons: L is the only answer that looks like the result of dividing something by x - 1. (Also: the leading term of a quotient is the quotient of the leading terms, so whatever the answer is, its leading term must be (3x^2)/x = 3x, and only L fits the bill.)

In 19, just compute the product, or note that its leading term is 9x^2 and only Y has this property, so it's Y.

In 20, the area of a square with side length S is S*S so (x+3)(x+3). If you expand this out you find it is N. (Without doing the calculation you can see it has to have leading term x^2, which really reduces the number of possibilities.)

Hopefully this answer has given you not just the answers, but some strategies and tips you can use on multiple choice problems. It is helpful--- especially under time pressure--- to exploit the multiple choice format for all it is worth. Often you do not have to solve a problem all the way to pick the only answer that could possibly be right from a group.

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September 9th, 2009 in DVD+RW | tags: dvd, dvd+rw, dvdduallayer, mac, media

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