Semester 1 Final Exam Review (Math 3)

Front

Simplify: (4+7i)(5+3i)

Back

-1 + 47i

Front

What are the solutions to the equation x^2 - 5x + 25 = 0?

Back

x = \frac{5 \pm 5i \sqrt{3}}{2}

Front

Given that (x+2) is a factor of the function f(x) = 5x^3 - 2x^2 - 20x + 8, which of the following is another factor?

Back

(x-2)

Front

Which best represents the end behavior of the function f(x) = 2x^5 + 3x^2 - 8x + 1?

Back

x \rightarrow \infty, f(x) \rightarrow \infty; x \rightarrow -\infty, f(x) \rightarrow -\infty

Front

What is the value of the function when x=4?

Back

6

Front

Definition of Complex Numbers

Back

A complex number is of the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as i^2 = -1.

Front

Definition of Polynomial Function

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_0 are constants and n is a non-negative integer.

Front

What is the Quadratic Formula?

Back

The solutions to the quadratic equation ax^2 + bx + c = 0 are given by x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

Definition of End Behavior of a Function

Back

End behavior describes the behavior of a function as x approaches positive or negative infinity.

Front

What is the Factor Theorem?

Back

The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).