<h3>
Answer: -2</h3>
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Explanation:
We use the remainder theorem. This is the idea where if we divide P(x) over (x-k), then the remainder is P(k).
Comparing x+1 to x-k shows that k = -1
It might help to rewrite x+1 as x-(-1) to get it into the form x-k better.
Plug this k value into the function
f(x) = 2x^6 + 3x^5 - 1
f(-1) = 2(-1)^2 + 3(-1)^5 - 1
f(-1) = 2(1) + 3(-1) - 1
f(-1) = 2 - 3 - 1
f(-1) = -1 - 1
f(-1) =-2
The remainder is -2
We can confirm this through synthetic division or polynomial long division.
Let, Number of multiple choice = x
Number of short answer question = y
Now, x + y = 20
& 3x + 11y = 100
Multiply 1st equation by 3, and subtract from eq,2,
3x + 3y = 60
After subtraction,
8y = 40
y = 40/8
y = 5
Now, substitute in eq (1),
x + 5 = 20
x = 15
In short, There are 15 Multiple choice & 5 short answer questions
Hope this helps!
Answer:
option f
option a
option d
option c
option e
option b
Step-by-step explanation:
we have x^2 - 6x + 7 = 0
f) x^2 - 6x = -7
a) x^2 - 6x + 9 = -7+9
d) (x-3)^2=2
c)
e) x-3=+-
b) x=3+-
