Algebra 2 – Unit 3: Polynomials & Exponent Rules

These flashcards review exponent laws, definitions and properties of polynomials, operations on polynomials, special products, and the procedure for polynomial long division.

What does the Product Rule of exponents state?

When multiplying powers with the same base, keep the base and add the exponents: a^m · a^n = a^{m+n}.

According to the Power Rule, how do you simplify (a^m)^n ?

Multiply the exponents: (a^m)^n = a^{m·n}.

How is the Power-of-a-Product Rule written?

(ab)^n = a^n · b^n for any real numbers a, b and integer n.

What is the Zero Exponent Rule?

Any non-zero base raised to the 0 power equals 1: a^0 = 1, a ≠ 0.

State the Negative Exponent Rule.

a^{-n} = 1 / a^n, so moving the factor to the opposite side of the fraction bar makes the exponent positive.

When simplifying negative exponents, which bases are moved?

Only the bases with negative exponents are moved across the fraction bar; positive-exponent bases stay where they are.

Define a polynomial.

An algebraic expression made of variables and numbers combined by addition or subtraction, whose variable exponents are non-negative integers.

What is a term of a polynomial?

A part of a polynomial separated from the others by a plus or minus sign.

How do you find the degree of a single term?

Add all exponents on the variables in that term; the sum is the term’s degree.

How is the degree of a polynomial determined?

It is the highest degree of any single term in the polynomial.

What does writing a polynomial in standard form mean?

Arranging its terms in descending order of degree (highest to lowest).

What is the leading coefficient of a polynomial?

The coefficient of the first term once the polynomial is written in standard (descending-degree) form.

List FIVE things NOT allowed in a polynomial.

Variables in denominators, negative exponents, fractional exponents, square roots of variables, or variables used as exponents.

How do you add or subtract polynomials?

Combine like terms—add or subtract coefficients of terms with the same variables and exponents.

What method is commonly used to multiply two binomials?

FOIL (First, Outer, Inner, Last) or general distribution of each term in one binomial across the other.

What is a polynomial with exactly two terms called?

Binomial.

What is a polynomial with exactly three terms called?

Trinomial.

What adjective describes any polynomial of degree 2?

Quadratic.

What special product is (x + y)(x – y)?

Difference of squares: x^2 – y^2.

Expand (x + y)^2.

x^2 + 2xy + y^2 (a perfect-square trinomial).

Expand (x – y)^2.

x^2 – 2xy + y^2 (a perfect-square trinomial).

Give the four key steps for polynomial long division.

1) Write missing powers with 0 coefficients. 2) Divide the leading terms to find the next quotient term. 3) Multiply, write beneath, and subtract (change all signs). 4) Repeat until the remainder’s degree is less than the divisor’s.