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gulleraliyeva1999
26.07.2019 •
Mathematics
Which of the following is a factor of 6x^3 + 6?
a) x - 1
b) x + 1
c) x² - 2x + 1
d) x² + x + 1
Solved
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Ответ:
B
Step-by-step explanation:
Given
6x³ + 6 ← factor out 6 from each term
= 6(x³ + 1)
x³ + 1 is a sum of cubes and factors as
x³ + 1 = (x + 1)(x² - x + 1)
Hence
6x³ + 6 = 6(x + 1)(x² - x + 1)
With factor (x + 1) → B
Ответ:
b) x + 1
Step-by-step explanation:
you can either
1) take (6x³ + 6) and divide by all the choices to see which one gives you a factor. You will realize that if you divide this by option b, you will be able to factorize the equation as follows:
(6x³ + 6) = 6(x+1)(x²−x+1)
Hence option b is a factor
or
2) (my preferred method), utilize the properties of functions and roots.
Let function f(x) = 6x³ + 6
any value of a which gives f(a) = 0 is a root , i.e (x-a) is a factor.
In this case, lets consider option b
let x + 1 = 0 > or x = -1
substitute this into the function f(x)
f(-1) = 6 (-1)³ + 6
f(-1) = -6 + 6 = 0
hence x = -1 is a root , or (x+1) is a factor.
as a sanity check, lets try choice a) x -1
let x - 1 = 0 > or x = +1
substitute this into the function f(x)
f(1) = 6 (1)³ + 6
f(1) = 6 + 6 = 12 ≠0
hence x = 1 is NOT a root , or (x-1) is NOT a factor.
You can do the same for c and d and find that they too are NOT factors.
Ответ:
The answer is A.
Step-by-step explanation:
Keeping point y as a reference, we know that it was rotated 180 degrees around the origin. I could tell this because y moved from one corner to another, if it was rotated 90 degrees it would move in a different direction. We also know it moved clockwise because if it moved counter clockwise it would have a different location.
We also know that it was shifted across the x-axis because it moved to the right. If it moved downwards it would have moved in the y direction.
Hope this helps.