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#### 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?

#### Is there a way to solve this system of equations without using the quadratic formula (or graphing)?

Is there a way to solve this system of equations without using the quadratic formula (or graphing)?

f(x) = –2/3 x + 4
g(x) = 3(x + 2)^2 – 4

How many solutions does the system above have? 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…)

#### In the equation below, the angle measures are in radians and a is a constant…

In the equation below, the angle measures are in radians and is a constant.

𝑠𝑖𝑛(𝜋/8)=𝑐𝑜𝑠(𝜋/𝑎)

Which of the following could be the value of ?

#### The country hall charges a rental fee of \$1000 and at least \$3000 for food. Olivia is planning a class reunion…

The country hall charges a rental fee of \$1000 and at least \$3000 for food. Olivia is planning a class reunion. If she had chosen a buffet that costs \$38.56 per person what is the minimum possible number of people who must attend to support the expense?

#### 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?

#### In the sequence above, each term after the first is equal to 1/3 of the term immediately before it…

27/5,9/5,3/5
38.In the sequence above, each term after the first is equal to 1/3 of the term immediately before it. what is the value of the first term in the sequence that is less than 1/20.