What are Expressions & Polynomials? 🤓
Let's begin by understanding the building blocks of algebra. Expressions and polynomials are fundamental to solving equations and modeling real-world problems.
- **Term:** A single number, a single variable, or a combination of numbers and variables multiplied together.
- **Variable:** A symbol (like $x$ or $y$) representing an unknown value.
- **Expression:** A collection of terms joined by addition or subtraction (e.g., $3x + 2$).
A **polynomial** is a special type of expression with one or more terms, where the variables have non-negative integer exponents. The name comes from *poly-* (meaning 'many') and *-nomial* (meaning 'term').
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Video: Advanced Expressions & Polynomials 🎬
This video will walk you through more complex topics, including combining like terms and applying the distributive property, with visual drawings on the canvas.
Practice Problems
Simplify the expressions below. Remember to combine like terms and distribute where necessary.
1) Simplify:
$3x^2 + 2x - 5 + x^2 - 4x + 1$
$3x^2 + 2x - 5 + x^2 - 4x + 1$
Answer:
2) Multiply:
$(x + 2)(x + 3)$
$(x + 2)(x + 3)$
Answer:
3) Simplify:
$4(2x-1) - 3(x+2)$
$4(2x-1) - 3(x+2)$
Answer:
4) Degree & Type:
$5x^3 - 2x + 7$
$5x^3 - 2x + 7$
Degree:
Type:
⚡ Polynomial Speed Quiz
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