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?

there are 50 questions on a quiz given to a class of a students…

there are 50 questions on a quiz given to a class of a students. Only 20% of the class answered all the questions on the quiz. Of the remaining students, half answered two-fifths of the questions and the other half answered three-fifths. What was the average number of questions answered on this quiz?

A question regarding the order you follow in the PWN guide for the Official SAT Tests…

Hello Mike,
I have a question regarding the order you follow in the PWN guide for the Official SAT Tests. Do you follow the order of the College Board website? I have a blue book The Official SAT Study Guide 2020 edition, with eight SAT tests. The order of the tests does not follow the same order as the one listed in the College Board website, and does not include tests 2 and 4 listed there. Thank you. Regards,
Elizabeth

In a certain class of 70 students, 4/7 of the students are boys, and the ratio of students 10 years or older to students less than 10 years is 2:3. If 2/3 of the girls are less than 10 years old, how many boys are 10 years old or older?

OK, so you have 40 boys and 30 girls. That’s easy enough to calculate because you’re given a part:whole ratio (boys to total students) and you already know the total number of students is 70. Be careful about the second ratio, though, because it’s a part:part ratio! If the ratio of older to younger is (more…)

The polygon ABCDEFGHI is a regular 9-sided polygon with consecutive vertices labeled in alphabetical order. What is the measure of angle ACE?

OK, so when you have a regular n-gon, you can figure out each angle in it using this formula: [(n-2)180]/n. In this case, 7*180/9 = 140, so we know each angle in the polygon is 140°. I couldn’t draw this quickly on the computer I’m on, so I found a good n-gon picture to mark (more…)

Students in a Science lab are working in groups to build both a small and a large electrical circuit…

Students in a Science lab are working in groups to build both a small and a large electrical circuit. A large circuit uses 4 resistors and 2 capacitors, and a small circuit uses 3 resistors and 1 capacitor. There are 100 resistors and 70 capacitors available, and each group must have enough resistors and capacitors to make one large and one small circuit. What is the maximum number of groups that could work on this lab project?