Coefficient, Variable, and Constant

• A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y
• A Coefficient is a number used to multiply a variable, $8x$ means $8$ times $x$, so $8$ is a coefficient
• A Constant is a number on its own

$$\begin{array}{ccccc}-2x^3& & +& & 5\\ \\ 1^{\text{st}}\text{ term}& & & & 2^{\text{nd}}\text{ term}\\ \text{Coefficient : −2}& & & & \text{5 called constant}\\ \text{Exponent of variable : 3}& & & & \text{Exponent of variable : 0}\end{array}$$

Polynomial

Monomial → The special names for polynomials with 1 term.

Example: $3x{y}^2,2x^5,4y,5x$

Binomial → The special names for polynomials with 2 terms.

Example: $7x-2,8x^2-3y,2x-4y^2,9a-b^4$

Trinomial → The special names for polynomials with 3 terms.

Example: $2x^2+3y-5z,5a^2+b+c^2,3i-2j+5k$

Expressing mathematical relationships algebraically

Example:

Write down an algebraic expression the following statements.

• Subtract twice the variable x from the product of 2x and y
• Multiply the square of y by 2x
• Add the cube root of the product of x and y to 4a

Solution:

• $2xy-2x$
• $2x{y}^2$
• $\sqrt[3]{xy}+4a$