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Factoring

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The process of writing a number or exponent as a product.

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Factorization

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Any combination of factors multiplied together resulting in the product

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Factors

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Any set of the numbers or expressions that form a product

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Prime factorization

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The unique factorization of a natural number written as a product of primes

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Greatest common factor GCF

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Product of all the common prime factors

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Relatively prime

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Expressions that share no common factors other then one

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GCF of monomials

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Product of the GCF of the coefficient and all common variables

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Factoring a polynomial

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The process of rewriting a polynomial as a product of polynomial factors.

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Factoring out the GCF

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The process of rewriting a polynomial as a product using the GCF of all of its terms.

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GCF of a polynomial

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The greatest common factor of all the terms of the polynomial.

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Prime polynomial

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A polynomial with integer coefficients that cannot be factored as a product of polynomials with integer coefficients other than 1 and itself.

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Factor by grouping

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A technique for factoring polynomials with four terms

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Root

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A solution to a quadratic equation in standard form

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Double root

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A root that is repeated twice

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Area of rectangle

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A = lw, where l represents the length and w represents the width.

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Area of square

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A = s2, where s represents the length of each side.

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Area of triangle

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A=1/2 bh, where b represents the length of the base and h represents the height.

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Area of circle

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A = πr2, where r represents the radius and the constant π ≈ 3.14.

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Exponential form

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An equivalent expression written using a rational exponent.

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Product rule for exponents

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xm ⋅ xn = xm+n; the product of two expressions with the same base can be simplified by adding the exponents

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Quotient rule for exponents

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The quotient of two expressions with the same base can be simplified by subtracting the exponents

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Power rule for exponents

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(xm)n = xmn; a power raised to a power can be simplified by multiplying the exponents.

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Power rule for a product

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(xy)n = xnyn; if a product is raised to a power, then apply that power to each factor in the product.

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FOIL

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When multiplying binomials we apply the distributive property multiple times in such a way as to multiply the first terms, outer terms, inner terms, and last terms.

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Check by evaluating

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We can be fairly certain that we have multiplied the polynomials correctly if we check that a few values evaluate to the same results in the original expression and in the answer.

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Square Root

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The number that, when multiplied by itself, yields the original number.

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Principle Square Root

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The positive square root of a real number, denoted with the symbol √.

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Radicand

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The expression a within a radical sign, an.

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Cube Root

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The number that, when used as a factor with itself three times, yields the original number; it is denoted with the symbol 3.

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Index

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The positive integer n in the notation n that is used to indicate an nth root.

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N th Root

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The number that, when raised to the nth power, yields the original number.

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Radical

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Used when referring to an expression of the form an .

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Principle n th Root

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The positive nth root when n is even.

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Product Rules for Radicals

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a⋅bn=an⋅bn, where a and b represent positive real numbers.

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Quotinct Rules for Radicals

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a b n= an bn , where a and b represent positive real numbers.

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Simplified Radicals

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A radical where the radicand does not consist of any factor that can be written as a perfect power of the index.

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Radical Expression

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An algebraic expression that contains radicals.

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Square Root Function

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The function f(x)=(square root)x

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Cube root function

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The function f(x)=x3.

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Like Radicals

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Radicals that share the same index and radicand.

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Similar Radicals

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Term used when referring to like radicals.

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Conjugates

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The factors (a + b) and (a − b) are conjugates.

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Rationalizing the Denominator

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The process of determining an equivalent radical expression with a rational denominator.

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Rational Exponents

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The fractional exponent m/nthat indicates a radical with index n and exponent m: am/n=amn.

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Exponential Form

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An equivalent expression written using a rational exponent.

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Radical Equation

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Any equation that contains one or more radicals with a variable in the radicand.

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Squaring Property of Equality

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Given real numbers a and b, where a = b, then a2 = b2.

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Extraneous Solution

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A solution that does not solve the original equation.

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Power Property of Equality

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Given any positive integer n and real numbers a and b, where a=b,then an=bn

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Root

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A solution to a quadratic equation in standard form.

College Algebra 3

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