CPhill

OBT -  The general rule is to first take out any GCF

So we have

16 - 2x^2

2 [ 8 - x^2 ] which factors as

2  [ √8  -  x ]  [ √8 + x ]        note  √8   = 2√2

2 [ 2√2 - x ]   [ 2√2 + x ]

Note that WolftamAlpha  tends to support the same result as one of its answers :

https://www.wolframalpha.com/input/?i=16+-+2x%5E2

BTW.........the "correct"  factorization  is sometimes ambiguous.....!!!!!

Your answer is just as "correct"  as the book's......

https://www.wolframalpha.com/input/?i=(4%2B+sqrt+(2)x+)+(4+-+sqrt+(2)x)

 x^4 + 9x^3 + 15x^2 + 9x + 14

Split  15x^2  into  14x^2  +  x^2

 x^4 + 9x^3 + 14x^2 + x^2 + 9x + 14     factor as

x^2  [x^2 + 9x + 14 ]  +  1 [ x^2 + 9x + 14 ]   take out GCF

[ x^2 + 1 ] [ x^2 + 9x + 14 ]

[ x^2 + 1 ] [  x + 7 ] [ x + 2 ]

Area of one dollar bill  =  100.75 cm^2

Area of 1 billion of them  =  100750000000 cm^2 =  1.0075 x 10^11    (1)

Number of sq cm to 1 sq mi  ≈  2.59 x 10^10  cm^2      (2)

So.....the answer is given by  (1) / (2)   ≈  3.9  sq mi    

5x-y  ≤   3    add y to both sides, subtract 3 from both sides

5x - 3 ≤  y 

This has infinite solutions

Here's a graph :  https://www.desmos.com/calculator/nhze0jzy7c

The green shaded area represents the solution area

Let the time she travels at 12 mph  = x minutes and if she trqvels back at 36 mph.....since this is 3 times as fast...it must take her x / 3 minutes  to return

So

x +  x/3  =  60     mutiply through by 3

3x + x  =  180

4x  = 180   divide by 4

45  = x

So....she travels   45/3 minutes = 15 minutes at 36 mph

And since  15 minutes = 1/4 hr......the distance is

Rate x Time  =  36mph  x 1/4 hr  =  9 miles

HAHAHA!!!!!......you guys/girls are too much....!!!!!

One more

Prove that

 sin  x

______   =   6         [ cancel the n's   and we have ]

     n 

si  x      =    6

-1 / 3

654 - (- 467 )  =  $1121

Desomos uses a little different notation.....here is the greatest integer function :

https://www.desmos.com/calculator/x7m8hhcrx6

Here's 1

We don't need much math here.....if 5 members paint the wall in 27 minutes.....3 times as many workers - 15 -  must take 1/3 as long  = 9 minutes

Here's 2

8 workers  -  5000 sq ft   -   30 minutes

Here's the way I like to think of these.......in one minute....the 8 workers would paint 

5000/ 30  =  500/3 sq ft...so....to paint 8000 sq ft would take   (8000) / (500/3)  =

8000 * 3 / 500  =    48 minutes

Here's the last one : 

Using the same approach as 2...we have

12 -  2400   - 45

In 1 minute, the 12 members paint  2400/45  = 160/3 sq ft

So...1 worker can paint (1/12)  of this  = ( 160/3 ) (1/12)  = 160 / 36 sq ft

So....in 1 minute  9 workers can paint 9 times as much  =  9 * 160 / 36  =  40 sq ft

So....it will take 9 workers    3600 / 40   =  90 minutes to paint 3600 sq ft