Find the quotient when x2 + 10x + 21 is divided by x + 7
1 answer:
<h3>Answer: x+3</h3>
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Work Shown:
x^2+10x+21 factors to (x+3)(x+7) since
7+3 = 10 and 7*3 = 21
Or you can use the FOIL rule to see that (x+3)(x+7) expands to x^2+10x+21
When we divide x^2+10x+21 over x+7, we get,
a pair of (x+7) terms cancel out when we divide
The quotient is x+3
The remainder is 0
See the diagram below for the long division table
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<h3>Answer: -10 and -40</h3>
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Explanation:
a = 200 = first term
d = -30 = common difference
Tn = nth term
Tn = a + d(n-1)
Tn = 200 + (-30)(n-1)
Tn = 200 - 30n + 30
Tn = -30n + 230
Set Tn less than 0 and isolate n
Tn < 0
-30n + 230 < 0
230 < 30n
30n > 230
n > 230/30
n > 7.667 approximately
Rounding up to the nearest whole number gets us
So Tn starts to turn negative when n = 8
We can see that,
Tn = -30n + 230
T7 = -30*7 + 230
T7 = 20
and
Tn = -30n + 230
T8 = -30*8 + 230
T8 = -10 is the 8th term
and lastly
Tn = -30n + 230
T9 = -30*9 + 230
T9 = -40 is the ninth term
Or once you determine that T7 = 20, you subtract 30 from it to get 20-30 = -10 which is the value of T8. Then T9 = -40 because -10-30 = -40.