Piqosity - Adaptive Practice Tests for the ISEE, ACT, and SAT.

Multiplying Polynomials

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.

Definition of a Polynomial and Classifications

$dx^3+ax^2+bx+c$

Contains 1 or more terms in the expression
d is the coefficient for the variable 𝑥³
a is the coefficient for the variable 𝑥²
b is the coefficient for the variable 𝑥
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 𝑥³,𝑥²,𝑥. (i.e. xy², f², g³, h⁷, 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.

Multiplying Polynomials

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.

Multiplying Polynomials on the ISEE

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 ≠ a²+ b²
(a + b)³ = (a + b)(a + b)(a + b)	(a + b)³ ≠ a³+b³

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)