5.1A Homework

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 3x^2 - 2x + 1 is a polynomial.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x + 5, the degree is 3.

Front

Classify the polynomial: 3x^2 - 8x + 1

Back

Quadratic (degree 2)

Front

What is standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 7x - 9 is in standard form.

Front

Identify the leading coefficient of the polynomial m(x) = x^5 - 3x^4 - x^3 + 3x^2.

Back

1 (the coefficient of the highest degree term, x^5)

Front

Classify the polynomial: 12

Back

Constant (degree 0)

Front

Classify the polynomial: -x^2 + x^9

Back

9th Degree Binomial (two terms, highest degree is 9)

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 5 is a binomial.

Front

What is a leading term in a polynomial?

Back

The leading term is the term in a polynomial that contains the highest power of the variable. For example, in 2x^4 + 3x^2, the leading term is 2x^4.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 5x is a monomial, while 5x + 3 is a polynomial.