<h2>
Question:</h2>
Find k if (x+1) is a factor of 2x³ + kx² + 1
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Answer:</h2>
k = 1
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Step-by-step explanation:</h2>
The factor of a polynomial F(x) is another polynomial that divides evenly into F(x). For example, x + 3 is a factor of the polynomial x² - 9.
<em>This is because;</em>
i. x² - 9 can be written as (x - 3)(x + 3) which shows that both (x - 3) and (x + 3) are factors.
ii. If x = -3 is substituted into the polynomial x² - 9, the result gives zero. i.e
=> (-3)² - 9
=> (9) - 9 = 0
Therefore, if (x + a) is a factor of a polynomial, substituting x = -a into the polynomial should result to zero. This also means that, if x - a is a factor of a polynomial, substituting x = a into the polynomial should give zero.
<em><u>From the question</u></em>
Given polynomial: 2x³ + kx² + 1
Given factor: x + 1.
Since x + 1 is a factor of the polynomial, substituting x = -1 into the polynomial should give zero and from there we can calculate the value of k. i.e
2(-1)³ + k(-1)² + 1 = 0
2(-1) + k(1) + 1 = 0
-2 + k + 1 = 0
k - 1 = 0
k = 1
Therefore the value of k is 1.
To solve for the A or the principal amount plus interest you can use two formulas:
A = P + I
Where: P = Principal
I = Interest
or you can use
A = P (1+ rt)
Where: P = principal
r = rate in decimal
t = time in years
With your given you can use the second one, without having to use the first.
Given that the Principal amount is $222 and the rate is 12% and time is 10 years, we first need to convert your rate into decimal by dividing the value in percent by 100 which will yield 0.12.
Then now we can just input the data that you know into the formula:
A = P(1+ rt)
= $222(1 + (0.12)(10))
= $222(2.2)
= $488.40
Your A is then equal to $488.40
If you need to get the simple interest all you need to use is the first formula given:
A = P + I
for the interest you transpose the P to the side of the A and you will get:
I = A - P
= $488.40 - $222
= $266.40
$266.40 is the added interest to the principal amount.
Answer:
13
Step-by-step explanation:
convert 52% into a decimal which is 0.52 then mulitply by 25 to get your answer
5 1.2
-3 7
6 1.2
2 -3
yes its a function, as long as the domain (input) doesnt have the same number with two different ranges (outputs) its a function
Answer:
Check it below
Step-by-step explanation:
1) The Boxplot is a visual tool to easily find the quartiles of a Distribution. To construct a boxplot it's necessary to organize the data, find at least the upper (3rd Quartile) and lower quartile (1st Quartile), and register the maximum and the minimum value.
2) This graph confirms that the South American ones have much more water than the North American counterparts. Notice the Upper Quartile, (the top of the box) for the Southern ones, it's over 100,000 yrds³. And Compare to the Northern one.
