8E Unit 5: Polynomials Flashcard

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 expression.

Front

How do you classify polynomials by degree?

Back

Polynomials can be classified as: Constant (degree 0), Linear (degree 1), Quadratic (degree 2), Cubic (degree 3), and so on.

Front

What is the sum of (2x^2 + 5x - 7) and (3 - 4x^2 + 6x)?

Back

The sum is -2x^2 + 11x - 4.

Front

How do you simplify the expression x^3(2x^2 + 3x)?

Back

The simplified expression is 2x^5 + 3x^4.

Front

What is an explicit formula for an arithmetic sequence?

Back

An explicit formula for an arithmetic sequence is a formula that allows you to find the nth term directly, such as a(n) = a + (n-1)d, where a is the first term and d is the common difference.

Front

What is the common difference in the sequence 2, 5, 8, 11?

Back

The common difference is 3.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system.

Front

Is the origin (0,0) a solution to the system of inequalities y > x and y < -x?

Back

No, the origin is not a solution because it does not satisfy either inequality.

Front

What is the result of adding two polynomials?

Back

The result of adding two polynomials is obtained by combining like terms.