Match each part of the expression with what it represents

The monomial x would be the length of the sports banner.

-We know this because we typically use a basic variable for the thing that does not change. In this case, the length of the sports banner remains the same.

The second degree term in the expression would be the increase in area of the culture banner to make the sports banner.

-We can tell this because when we increase the width of the banner by 12, the resulting polynomial is 12x larger than x^2 (which was the original area of the culture banner.

The binomial expression x + 12 would be the width of the sports banner.

-Since we are increasing the width of the culture banner from x, x + 12 would represent the new width of the sports banner.

The first degree term in the expression would be the area of the culture banner.

-Because side of the culture banner is the same before the increase, multiplying x by itself will give you an area of x^2. This is the first degree term.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}