Front

What are the factors of the polynomial f(x) = x^3 - 6x^2 - 4x + 24?

Back

The factors are (x + 2), (x - 2), and (x - 6).

Front

How many complex roots does the polynomial y = x^2 + x - 2 have?

Back

The polynomial has 2 complex roots.

Front

What is a perfect square binomial?

Back

A perfect square binomial is a polynomial that can be expressed as (a + b)^2 = a^2 + 2ab + b^2.

Front

Which polynomial can be factored as a perfect square binomial?

Back

x^2 + 6x + 9 can be factored as (x + 3)^2.

Front

What is the product of a complex number and its conjugate?

Back

The product of (a + bi) and (a - bi) is a^2 + b^2.

Front

Find the product of (2 + 5i) and its conjugate (2 - 5i).

Back

The product is 29.

Front

How do you simplify the expression (4 + 7i) + (6 - i) - (3 - 2i)?

Back

The simplified expression is 7 + 8i.

Front

What is the definition of a complex number?

Back

A complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a) for the equation ax^2 + bx + c = 0.