Polynomials and Quadratics Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

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

Front

How do you factor a quadratic polynomial?

Back

To factor a quadratic polynomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the polynomial as (px + q)(rx + s).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What is the result of (3x^3 + 3x^2 - 4x + 5) + (x^3 - 2x^2 + x - 4)?

Back

The result is 4x^3 + 1x^2 - 3x + 1.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms.

Front

What is the result of (5x + x^2 - 4) - (4x - x^2 + 6)?

Back

The result is 2x^2 + x - 10.

Front

What is the product of (3x + 2)(2x + 4)?

Back

The product is 6x^2 + 16x + 8.