Coolmath Algebra by Karen at Coolmath.com
Algebra Crunchers
Coolmath's Algebra Practice Problems-
Polynomials:
 
Substituting numbers into polynomials
Example: Given x^2+3x-7 let x = -2		 Adding and subtracting polynomials
Example: ( 5x^2+3x-7 ) - ( 9x^3-3x^2-8x+6 )
Exponent rules for multiplying polynomials 1
Example: Simplify ( x^2 )( y^5 )( x^3 )( y )		 Exponent rules for dividing polynomials
Example: Simplify ( ( x^2 )( y^5 )( w^3 ) ) / ( ( x^7 )( y^2 )( w^8 ) )
Exponent rules for multiplying polynomials  with negative exponents
Example: Simplify ( x^-8 )( y^-5 )( x^3 )( y^2 )		 Exponent rules for multiplying powers of exponents
Example: Simplify ( x^2 )^5 ( w^3 )( x^7 )^2 ( w^4 )^8
Exponent rules for dividing polynomials with negative exponents
Example: Simplify ( ( x^-4 )^6 ( y^-3 )( w^2 )^5 ) / ( ( x^-5 )( y^7 )^-2( w^-8 ) )		 Exponent rules for multiplying powers of exponents with negative exponents
Example: Simplify ( x^-2 )^3 ( w^-5 ) ( x^4 )^-6 ( w^2 )^8
Exponent rules for polynomials
Example: Simplify ( ( x^8 )( y^5 )( x^3 )( y ) )^2		 Exponent rules for polynomials with negative exponents
Example: Simplify ( ( x^-3 )( y^5 )( x^4 )( w^-6 )( y ) )^-1
Multiplying binomials - FOIL
Example: ( 5x+3 )( 2x-1 )		 Multiplying harder polynomials
Example: ( 2x-3 )( 5x^2-7x+1 )
Factoring trinomials with no number in front of the x-squared
Example: Factor x^2-3x-10		 Factoring trinomials with two prime numbers
Example: Factor 2x^2-13x-7
Factoring trinomials with one prime number
Example: Factor 6x^2-17x+5		 Factoring trinomials with no primes
Example: Factor 8x^2+2x-15
Factoring - the difference of two squares
Example: Factor 9x^2-25		 Factoring - the sum of two squares (factoring with complex numbers)
Example: Factor x^2+9
Factoring - the sum and difference of two cubes
Example: Factor 27x^3-1		 Factoring - factor by grouping
Example: Factor 15ab+20ay-6bx-8xy

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