The value of k is 2 if the polynomial x³ - 3x² - 10x + 24 is divided by the expression (x - 2).
<h3>What is synthetic division?</h3>
In the case of dividing by a linear factor, the synthetic division is a shorthand, or quicker, a technique of polynomial division.
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We have a polynomial:
x³ - 3x² - 10x + 24
Which is divided by (x - 2)
We can divide using the synthetic division:
The first row: 1 -3 -10 24
The entry outside the row: 2
The missing value which is 2
k = 2
Thus, the value of k is 2 if the polynomial x³ - 3x² - 10x + 24 is divided by the expression (x - 2).
Learn more about the synthetic division here:
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We have been given that the number of species of coastal dune plants in Australia decreases as the latitude, in °s, increases.
Further we know that there are 34 species at 11°s and 26 species at 44°s.
We can express the given information at two ordered pairs as shown below:
Let us find slope of the line through these points:
Therefore, we can write the equation of line in slope intercept form as:
Where b is the y intercept, and we can find its value using one of the two points.
Therefore, the required equation of the linear function is:
Hope this isn't too confusing
All of the numbers have different shortcuts.
1. Yes. Divisible by 4: if last two digits are divisible by 4 then the whole number is yes)
2. No. Divisible by 6: it must be even and when you add them up, (44) it must be divisible by 3 (no, 44 is not divisible by 3)
3. Divisible by 8: ( last 3 numbers are divisible by 8 (312) = 39 ( yes it is)
4 Yes. Divisible by 11: ( sum of digits at odd places and sum of digits at even spaces,is either 0 or divisible by 11) yes, 278949. (2+8+9) + (7+9+9)= 19 + 25 = 44 and 44 is divisible by 11)
5. No. Divisible by 12 (divisible by 3 and 4, sum of digits is divisible by 3 ; and last 2 digits divisible by 4: 87654395 : 52/3= 18 (yes) 95/4(no) this number not divisible by 12
6. No. Divisible by 15: divisible by 3 and 5 ..87654385 = 46/3 = 15..(No) divisible by 5 yes. The number is not divisible by 15