@Amitre yes, this follows from the remainder theorem.
It is also worth knowing that r is a root of polynomial p(x) if and only if x-r is a factor of p(x) (that is, p(x) = (x-r)q(x) for some polynomial q(x)).
Also, use p or p(x) – it is not p times ().
Thank you guys
Yes, the factor theorem and the remainder theorem are all useful. For last minutes studying, you might find the following videos very helpful!
Every polynomial can be written using the division algorithm for polynomials as P(x)=(x-a)Q(x)+r(x) where Q(x) is a polynomial of degree n-1 when P(x) is of degree n. Then, r(x) has to be a constant in this particular case because it has to be of lower degree than (x-a), therefore, r(x) is of degree 0, hence a constant.
So, we have:
P(x)=(x-a)Q(x)+r for a constant r.
Then, if (x-a) is a factor of P(x), then, P(a)=0 meaning, 0=P(a)=(a-a)Q(a)+r so, 0=0+r, that is, the remainder r must be zero if in fact (x-a) is a factor of P(x).
Moreover,
If (x-a) is not a factor, we have:
P(a)=(a-a)Q(a)+r which implies
P(a)=r, which is in fact the case. That is, when you divide a polynomial by x-b, then, either P(b)=0, that is, x-b is a factor, or P(b)=r which is that the value of the remainder is the value of the function at x=b.
Hope this helps!
Hi there,
there is this one problem that I am stuck on for some reason. Would be grateful if anyone can help.
So there is a circle with a radius of two and it has an arc. IN the figure, points A and B lie on the circle with center O. If the length of minor arc AB is less than pi/2 but grater than pi/4, what is one possible value of x
nvm I figured it out any number between 22.5 and 45 would work.
Here is another problem:
A group of people were asked if they are or are not registered organ donors. An equal number of men and women were surveyed and partial results of the data are shown. Three times as many men responded that they were not registered organ donors than men who responded that they were registered organ donors, and fifty more women responded that that they were not registered organ donors than women who responded that they were registered organ donors. If an individual is selected at random from this group, what is the probability that the person is a man who is a registered organ donor. There are total of 350 organ donors and a total of 650 not organ donors.
As is almost always the case, you can puzzle this out without using algebra (though algebra might be quicker).
We need 300 more non-donors than donors. From the women, we get 50 more. So we need 250 more from the men. Since there are three times as many non-donor men than donor men, we need a number that when tripled, gives us the 250 surplus. You may realize that double the number must be 250 or you may do trial and error to land on 125 donor men, 375 non-donor. So 500 men over all, 1000 people total and 125 who are male donors.
I’ll let someone else post an algebra-based answer. Where is the problem from?
A thread filled with math problems 
Are all the problems from the SAT or can there be other types of math problems? Either way, I’m definitely going to be working through them in the next few days.
You are great!
I used 375 and found that both C and E worked. I was confused at first until I saw “the next larger integer”. I guess you have to make sure you read the question right.
I have a question about rounding/correct answer. In an answer explanation, it says x=274.2 minutes. You’re supposed to “round to the nearest 5 minutes”, so x is 275.
However, the book says the correct answer is 270, even though the explanation says its 275… Is the correct answer 275??
274.2 minutes rounded to the nearest 5 minutes is 275 minutes.
I thought it would be nice to revive this thread and discuss some important SAT math problems. After I post each question I’ll give some time for you to post your attempted solutions before providing my own. I’ll also provide the Difficulty Level, Topic, and Subtopic for each one. Here is the first one:
Level 4, Heart of Algebra, Solving Linear Equations
The answer is C.For example,we take 75 as the number divisible by 15,25 then we are looking for the next multiple which is 150.Substract 75 from 150 and the answer is n+75,so it’s C.
About the problem 3 men and 3 women…the answer is…2
Find lcm of 15 and 25 then add that number to n that’s it