Math III EOC Review #3

Front

What is the simplest form of a fraction?

Back

A fraction is in simplest form when the numerator and denominator have no common factors other than 1.

Front

How do you convert a logarithmic equation to an exponential equation?

Back

To convert log_b(a) = c to exponential form, use b^c = a.

Front

What is the solution to the equation log_2(291) = 8 in exponential form?

Back

(2^8) = 291.

Front

How do you find the center of a circle given its equation in standard form?

Back

The center of a circle in the form (x-h)² + (y-k)² = r² is (h, k).

Front

What is the center of the circle with the equation x² + (y+6)² = 196?

Back

(0, -6).

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial p(x) by (x-c) is p(c).

Front

How do you find the remainder when dividing a polynomial by a linear factor?

Back

Evaluate the polynomial at the root of the linear factor.

Front

What is the value of p(6) for the polynomial p(x) = 7x³ - 36x² - 42x + 30?

Back

p(6) = -6.

Front

What does it mean for a fraction to be in simplest form?

Back

It means that the numerator and denominator are coprime (no common factors).

Front

What is the process to solve for x in an equation?

Back

Isolate x on one side of the equation using inverse operations.