Unit 5 Test Review

Front

What is the factored form of the polynomial 8a^3 + 4a^2 - 2a - 1?

Back

(2a+1)(4a^2-2a+1)

Front

Define 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 the degree of the polynomial 4a^3 - 3a^2 + 2?

Back

The degree is 3, which is the highest exponent of the variable a.

Front

What does it mean for a polynomial to be factored?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the zero-product property?

Back

If the product of two or more factors is zero, at least one of the factors must be zero.

Front

How do you find the roots of a polynomial?

Back

To find the roots, set the polynomial equal to zero and solve for the variable.

Front

What is the difference between a monomial and a binomial?

Back

A monomial is a polynomial with one term, while a binomial has two terms.

Front

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

Back

The leading coefficient is 5, which is the coefficient of the term with the highest degree.

Front

Explain the process of polynomial long division.

Back

Polynomial long division involves dividing the leading term of the dividend by the leading term of the divisor, multiplying the entire divisor by that result, subtracting, and repeating the process.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used when dividing by a linear factor.