Algebra 1, Unit 6: Exponents and Polynomials. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What does an exponent tell you to do with the base number?
- Multiply the base by itself that many times
- Simplify: x^3 times x^4
- x^7 (add exponents when multiplying same base)
- Simplify: x^8 / x^3
- x^5 (subtract exponents when dividing same base)
- Simplify: (x^3)^2
- x^6 (multiply exponents when raising a power to a power)
- What does a negative exponent indicate, such as x^-2?
- The reciprocal of the base raised to the positive exponent (1/x^2)
- What is x^0 equal to, for any nonzero x?
- 1
- Simplify: (2x)^3
- 8x^3 (distribute the exponent to each factor)
- What is scientific notation used for?
- Writing very large or very small numbers concisely using powers of 10
- Write 3,400,000 in scientific notation
- 3.4 x 10^6
- Write 0.00056 in scientific notation
- 5.6 x 10^-4
- What is a polynomial?
- An expression with multiple terms, each a coefficient times a variable raised to a whole number power
- What is the degree of a polynomial?
- The highest exponent among its terms
- What is a leading coefficient?
- The coefficient of the term with the highest degree
- Add: (3x^2 + 2x) + (x^2 - 5x)
- 4x^2 - 3x
- Subtract: (5x^2 + 3) - (2x^2 - 1)
- 3x^2 + 4
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