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
The rounded value is option B) 6.03 which is rounded to the nearest hundredth.
<u>Step-by-step explanation:</u>
- To find the value of 8.3 x 24.2 x 0.03, we need to multiply the given numbers to get a decimal value.
- And then, after getting the value of 8.3 x 24.2 x 0.03 it should be rounded to the nearest hundredth.
<u>So, let's multiply the numbers first :</u>
8.3 × 24.2 × 0.03 = 6.0258
The value is 6.0258
<u>To round the value 6.0258 to the nearest hundredth :</u>
- The first number next to the decimal point represents the tenth.
- The second number next to the decimal point is the hundredth.
- The third number next to the decimal point is thousandth.
Therefore, to round the value to the nearest hundredth, look for the thousandth number is either less than 5 or greater and or equal to 5.
If, thousandth place is greater or equal to 5, then the hundredth number should be increased by 1.
The hundredth is 6.02 and the number in the thousandth place is 5. So add 1 to the hundredth place.
The value is rounded to 6.03 to the nearest hundredth.
Answer: 2x
^4
+7x−4x
^2
−4
Step-by-step explanation:
2x
^4
−x*3−4x
^2
+10x−4
2x
^4
−3x−4x
^2
+10x−4
2x
^4
+(−3x+10x)−4x
^2
−4
2x
^4
+7x−4x
^2
−4
Answer:
10 miles per 1 minute
Step-by-step explanation:
100 miles / 10 minutes
100/10
10/1
10 miles / 1 minute
4+1, 3+2, 2+3, 1+4. 4 total combinations, unless 4+1 and 1+4 are the same. In that case, there are only 2, 1+4, and 2+3
