Algebraic expressions can be made up of one or more terms, which are either added or subtracted from each other. These are known as polynomials and can include one or more variables, their exponents, and known numbers called constants.

- Contains 1 or more terms in the expression
*d*is the coefficient for the variable 𝑥^{3}*a*is the coefficient for the variable^{2}*b*is the coefficient for the variable*c*is the constant (number: 4, 10, -5, etc.)

**Keep In Mind**

- Coefficients and the constant,
*c*, can be ANY real number. - When listing the variables, ANY variables with their own distinct exponents can be used in place of 𝑥
^{3},^{ }𝑥^{2},^{ }𝑥. (i.e.*xy*^{2},*f*^{2},*g*^{3},*h*^{7},*z*, etc. - A lone constant (i.e. 2, -15, 1.4) CAN be classified as both a polynomial AND a monomial.
- Polynomials with more than 4 terms exist but are unlikely to be tested on the ISEE.

While true polynomials always contain positive, whole number exponents, the ISEE can include rational (fractional) exponents.

**Depending on their number of terms, a polynomial can be further classified as a monomial, binomial, or trinomial. **

Each of the following methods is a variation of the distributive property.

Choose the method that is most intuitive for you; the following examples will focus on multiplying binomials.

Quadratics are fairly common on the ISEE so expect to see multiplication of binomials.

When you encounter polynomial expressions that have been raised to an exponent, write out the terms and avoid this common mistake:

Correct |
Incorrect |

(a + b)^{2} = (a + b)(a + b) |
(a + b)^{2} ≠ a^{2 }+ b^{2} |

(a + b)^{3} = (a + b)(a + b)(a + b) |
(a + b)^{3} ≠ a^{3}+b^{3} |

Problems that involve multiplying polynomials with two or more terms OR multiplying more than two polynomials can also be tested. Continuing the example from above:

(*a *+ *b*)^{3} = (*a *+ *b*)(*a *+ *b*)(*a *+ *b*)

Some questions may ask for the coefficients of one or more variables several different ways.

The ISEE often integrates multiple topics together on test questions.

Some problems may ask you to incorporate polynomial multiplication when calculating the area or volume of geometric figures.

**Answers to Practice Questions**

- D
- A
- C
- B
- A

Create a free account below to start practicing nearly 7,000 adaptive questions.