U8D4 Polynomial Addition and Subtraction

Front

What is the degree of the monomial -47x^2y^5z?

Back

The degree is 8, calculated as the sum of the exponents: 2 (from x) + 5 (from y) + 1 (from z) = 8.

Front

A term containing just a number, but no variable factors, is called a __________.

Back

constant.

Front

Classify the polynomial x^2y - 7xy^2z + 14x by its degree.

Back

Quartic (4), since the highest degree term is -7xy^2z, which has a degree of 4.

Front

Simplify the expression (x^2 + 6x - 8) + (7 - 5x + 9x^2).

Back

10x^2 + x - 1.

Front

Perform the operation (3x^2 - 8x + 7) + (8x^2 + 9x - 16) and write the answer in descending order.

Back

11x^2 + x - 9.

Front

What is a polynomial?

Back

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

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a number, a variable, or a product of numbers and variables.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial.

Front

What is the difference between a polynomial and a monomial?

Back

A polynomial can have multiple terms, while a monomial has only one term.

Front

What is the leading coefficient of the polynomial 4x^3 - 2x^2 + 5?

Back

The leading coefficient is 4, which is the coefficient of the term with the highest degree.