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## Replies to: SAT Math Problems Thread

304Member1,289Senior Member12New MemberWhich of the following must be true about p x ( ) ?

A) x − 5 is a factor of p x ( ).

B) x − 2 is a factor of p x ( ).

C) x + 2 is a factor of p x ( ).

D) The remainder when p x ( ) is divided

by x − 3 is −2.

Can someone simplify the answer and the way.

1,289Senior MemberThe remainder when the polynomial p(x) is divided by x - r is p(r).

4,747Senior MemberIt 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 ().

12New Member2New Memberhttps://www.youtube.com/watch?v=3RLK5al9WCc

https://www.youtube.com/watch?v=8Rp_BuoimTQ

2New MemberSo, 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!

146Junior Memberthere 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

146Junior Member146Junior MemberA 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.

1,078Senior MemberWe 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?

119Junior MemberAre 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.

1New Member25Junior Member