Simplify (x3 + 3x2 + 5x – 4) – (3x3 – 8x2 – 5x + 6)
The first thing I have to do is take that "minus" sign through the parentheses containing the second polynomial. Some students find it helpful to put a "1" in front of the parentheses, to help them keep track of the minus sign.
Here's what the subtraction looks like, when working horizontally:
(x3 + 3x2 + 5x – 4) – (3x3 – 8x2 – 5x + 6)
(x3 + 3x2 + 5x – 4) – 1(3x3 – 8x2 – 5x + 6)
(x3 + 3x2 + 5x – 4) – 1(3x3) – 1 (–8x2) – 1(–5x) – 1(6)
x3 + 3x2 + 5x – 4 – 3x3 + 8x2 + 5x – 6
x3 – 3x3 + 3x2 + 8x2 + 5x + 5x – 4 – 6
–2x3 + 11x2 + 10x –10
And here's what the subtraction looks like, when going vertically:
x
3
−(3x
3
+3x
2
−8x
2
+5x
−5x
−4
+6)
In the horizontal addition (above), you may have noticed that running the negative through the parentheses changed the sign on each and every term inside those parentheses. The shortcut when working vertically is to not bother writing in the subtaction sign or the parentheses; instead, write the second polynomial in the second row, and then just flip all the signs in that row, "plus" to "minus" and "minus" to "plus".
\
x
3
–3x
3
−2x
3
+3x
2
+8x
2
+11x
2
+5x
+5x
+10x
−4
–6
−10
Either way, I get the answer:
–2x3 + 11x2 + 10x – 10
I'm pretty sure it is.
If i'm wrong, I'm truly sorry
Let x = angle we must find
tan x = 14/30
arctan(tan x) = arctan(14/30)
x = 25.0168934781
Answer: 25 degrees
Since there is a shortage in the budget in 2005 by 553,656,965,393.18, the total debt that of the United States in 2005 will be the public debt by 2004 added with this deficit in the budget. Having said that, the public debt by 2004 should be equal to,
$ 7.9327 x 10^12
