College Algebra Final

Front

Multiply: (4 – 3i)(7 + 2i)

Back

34 - 13i

Front

Simplify the expression: √(246x²)

Back

3x√2 - 2x√3 + 6x

Front

Identify the Rational Zeros of the polynomial: f(x) = 3x³ + 2x² - 6x + 7

Back

±1, ±7, ±1/3, ±7/3

Front

Evaluate log₅(20) to three decimal places.

Back

1.861

Front

What is the definition of a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

Define Rational Root Theorem.

Back

The Rational Root Theorem states that any rational solution of a polynomial equation is of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

What is the difference between a rational number and an irrational number?

Back

A rational number can be expressed as a fraction a/b, where a and b are integers and b ≠ 0. An irrational number cannot be expressed as a simple fraction.

Front

What is the formula for the sum of a geometric series?

Back

S_n = a(1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.