Five students divided 74 base-ten rods equally among them. how many base-ten rods were left over?
1 answer:
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one way would be to factor
I can't factor it so we will have to use Descartes' Rule of Signs which is helpful for finding how many real roots you have
it goes like this:
for a polynomial with real coefients, consider .
after arranging the terms in decending order in terms of degree, count how many times the signs of the coeffients change direction and minus 2 from that number until you get to 1 or 0. that will be the number of even roots the function can have
We have (-, -, +, +). the signs changed 1 times, so it has 1 real positive root
to get the negative roots, we evaluate f(-x) and see how many times the root changes
signs are (-, -, -, +). there was 1 change in sign
so the function has 1 real negative root
a total of 2 real roots
a function of degree can have at most,
roots
our function is degree 6 so it has 6 roots
if 2 are real, then the others must be complex
6-2=4 so there are 4 complex roots
you can also show that there are only 2 real roots by using a graphing utility to see that there are only 2 real roots
Answer:
Option b) is correct.
The completed factor of given expression is
Step-by-step explanation:
Given expression is
To find the completed factor for the given expression:
:
Taking the common number "2" outside to the above expression we get
Now rewritting the above expression as below
(since 16 can be written as the number 2 to the power of 4)
The above expression is of the form
Here and
Therefore it becomes
The above expression is of the form
Here and
Therefore it becomes
Therefore
Option b) is correct.
The completed factor of given expression is