Algebra 2A Final Review

Front

What is the result of dividing the polynomial 2x^3 - 5x^2 + 3x + 7 by (x - 2)?

Back

The result is 2x^2 - x + 1 + \frac{9}{x-2}.

Front

Factor the expression x^2 + 4x - 32.

Back

The factored form is (x + 8)(x - 4).

Front

Simplify the expression \sqrt[3]{320x^4y}.

Back

The simplified form is 4x\sqrt[3]{5xy}.

Front

What can be concluded about the roots of a quadratic equation with a discriminant of -2?

Back

The roots must be imaginary.

Front

Find the product of (8n - 1)(7n^2 - 3n - 4).

Back

The product is 56n^3 - 31n^2 - 29n + 4.

Front

What is the definition of a polynomial?

Back

A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the roots of a quadratic equation, given by \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, two imaginary roots.

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 difference between rational and irrational roots?

Back

Rational roots can be expressed as a fraction of two integers, while irrational roots cannot be expressed as such.