S1 Final exam Review Units 3, 4 and 5

Front

Simplify the expression: (-6 - 2i)²

Back

32 + 24i

Front

Factor the polynomial: f(x) = 2x³ - 9x² - 11x + 30

Back

(2x - 3)(x + 2)(x - 5)

Front

Simplify the rational expression: \frac{x² - 1}{2x² + x - 3} and state the excluded values.

Back

\frac{(x + 1)}{(2x + 3)}; x ≠ {-\frac{3}{2}, 1}

Front

Factor Completely: 3x⁴ + 3x³ - 12x² - 12x

Back

3x(x + 2)(x - 2)(x + 1)

Front

Find the sum: \frac{x}{x + 1} + \frac{2x}{x + 2}

Back

\frac{3x² + 4x}{(x + 1)(x + 2)}

Front

What is the definition of a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What are excluded values in rational expressions?

Back

Excluded values are values of the variable that make the denominator zero, leading to undefined expressions.

Front

What is the process of factoring a polynomial?

Back

Factoring a polynomial involves expressing it as a product of its factors, which can be simpler polynomials.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation: x = \frac{-b \pm \sqrt{b² - 4ac}}{2a}.