A phone plan costs 25 + 0.10m dollars, where m is the number of text messages. That little line of algebra holds every word of this unit: a variable (m), a coefficient (0.10), a constant (25) and two terms. Learn the names once and every polynomial question reads like plain English.
Every piece of an expression has a name
An algebraic expression is a math phrase made of numbers and letters joined by operations, like 5x² − 9x + 36. It has NO equals sign. Put an equals sign in, like y = m + 8, and it becomes an equation: something you can solve.
| Word | In 5x² − 9x + 36 |
|---|---|
| terms | 5x², −9x, 36 |
| variable | x |
| coefficients | 5 and −9 |
| constant | 36 |
| exponent | the 2 in x² |
A variable is a letter whose value can change: x, y, m. The coefficient is the number multiplying the variable in a term. In 5x² the coefficient is 5. In −9x it is −9: the sign in front of a term belongs to that term. If no number is showing, the coefficient is 1, so x² means 1x² and −y means −1y.
Tap the pieces of 5x² − 9x + 36 as Pip asks.
Tap the constant. 1 / 3
A constant is a term with no variable: just a number, like the 36 above. Its value never changes, which is why it is called constant. Terms are the pieces separated by + and − signs, so 4x² + 2x − 1 has three terms: 4x², 2x and −1.
Expression or equation? Look for the equals sign. 3x + 2 is an expression (you can simplify or evaluate it). 3x + 2 = 11 is an equation (you can solve it: x = 3).
Expression or equation? Tap a card, then its bin.
Algebra Basics: What Are Polynomials?
- How he splits an expression into terms at the + and − signs.
- What he calls the number in front of a variable.
- Pause when he shows a term with no number in front and say its coefficient.
Each tile is a term: the big square is x², the long bar is x, the little square is 1. Orange tiles are negative.