Exponents & Polynomials Review

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What is an exponent?

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An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

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What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 3x^2 + 2x - 5 is a polynomial.

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How do you multiply two polynomials?

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To multiply two polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms.

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What is the area of a rectangle?

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The area of a rectangle is calculated by multiplying its length by its width. For example, if the length is 4a^4b^5 and the width is 3a^2b^3, the area is 12a^6b^8.

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What is the power of a power property?

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The power of a power property states that when raising a power to another power, you multiply the exponents. For example, (x^a)^b = x^(a*b).

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How do you simplify (2x^3y)^6?

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To simplify (2x^3y)^6, apply the power of a product property: (ab)^n = a^n * b^n. Thus, (2^6)(x^(3*6))(y^6) = 64x^18y^6.

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What is the product of powers property?

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The product of powers property states that when multiplying two powers with the same base, you add the exponents. For example, x^a * x^b = x^(a+b).

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How do you add polynomials?

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To add polynomials, combine like terms by adding the coefficients of terms that have the same variable and exponent. For example, (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8) results in 3y^3 + 7y^2 - 4y + 3.

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What is the coefficient in a polynomial?

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A coefficient is a numerical factor in a term of a polynomial. For example, in the term 5x^2, 5 is the coefficient.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest exponent of its variable. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.