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?
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Multiply the base by itself that many times- Simplify: x^3 times x^4
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x^7 (add exponents when multiplying same base)- Simplify: x^8 / x^3
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x^5 (subtract exponents when dividing same base)- Simplify: (x^3)^2
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x^6 (multiply exponents when raising a power to a power)- What does a negative exponent indicate, such as x^-2?
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The reciprocal of the base raised to the positive exponent (1/x^2)- What is x^0 equal to, for any nonzero x?
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1- Simplify: (2x)^3
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8x^3 (distribute the exponent to each factor)- What is scientific notation used for?
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Writing very large or very small numbers concisely using powers of 10- Write 3,400,000 in scientific notation
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3.4 x 10^6- Write 0.00056 in scientific notation
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5.6 x 10^-4- What is a polynomial?
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An expression with multiple terms, each a coefficient times a variable raised to a whole number power- What is the degree of a polynomial?
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The highest exponent among its terms- What is a leading coefficient?
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The coefficient of the term with the highest degree- Add: (3x^2 + 2x) + (x^2 - 5x)
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4x^2 - 3x- Subtract: (5x^2 + 3) - (2x^2 - 1)
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3x^2 + 4
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