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at 7am a sewage treatment tank contains 3000000 gallons of water…

at 7am a sewage treatment tank contains 3000000 gallons of water. starting at 7am, x gallons per minute flow into the tank, and y gallons per minute flow out of the tank. no water enters or leaves the tank otherwise. which of the following functions f models the number of gallons of water in the sewage treatment plant at 8am?

In the “Proving Grounds” Quiz 1 #5 explanation, you state: “…We know that, as a general rule, the remainder when a polynomial f(x) is divided by x – a is f(a).” Can you explain this further?

In the “Proving Grounds” Quiz 1 #5, this question is given:

p(x) = ax^2 + bx + c
q(x) = ax^2 + bx + d

The functions p(x) and q(x) are defined above, and a, b, c, and d are constants. If x – 3 is a factor of p(x) and d is 8 greater than c, what is the remainder when q(x) is divided by x – 3?

In your answer explanation, you state:
“…We know that, as a general rule, the remainder when a polynomial f(x) is divided by x – a is f(a).”

Can you explain this further?

Try a chapter from the Math Guide Online for free

UPDATE: Now you can sign up for trial access (3 days) to the whole Math Guide Online. You can ignore the below. A bunch of folks have asked me if there’s a free trial for the new Math Guide Online. Well, at launch there wasn’t but now there is! You may now try before you (more…)

Available now: SAT Math Guide Online

For the past few months I’ve been working on an online, interactive version of PWN the SAT: Math Guide, and I’m excited to announce that subscriptions are available now in the PWN store!