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Algebra Review
Polynomials
More polynomials
sections 1.1 and 1.2
section 1.2 and 1.4
100
Classify square root of 16
What is a natural number, whole number, integer, rational number, and real number? Also complex number!!
100
The coefficient and degree for the monomial 5.
What is 5 and 0? (When a variable is not present, its degree is zero.)
100
The factored form of 60(x^2)y - 48x(y^2) + 72(x^3)y
What is 12xy(5x - 4y + 6(x^2))? (Remember to always factor out the common monomial first.)
100
An equation that is satisfied for every value of the variable for which both sides are defined is called ___________.
What is an identity?
100
Solve by factoring: 2(2x^2 - 4x) + 3 = 0
What is {1/2, 3/2}? (Solution: 4x^2 - 8x + 3 = 0 --> (2x-1)(2x-3)=0)
200
The property illustrated by (x + 2) +7 = x + (2 + 7). Be complete!
What is the associative property for addition?
200
The simplest form of 6(x^3 + x^2 - 3) - 4(2x^3 - 3x^2).
What is -2x^3 + 18x^2 - 18?
200
The factored form of (16x^2 + 8x + 1).
What is (4x + 1)^2? ((16x^2 + 8x + 1) is an example of a perfect square trinomial.)
200
The fact that 3x = 0 implies that x = 0 is a result of this property.
What is the zero product property? (Remember to use this property when solving an equation by factoring.)
200
Solve using the quadratic formula: 2x^2 + 5x + 3 = 0.
What is {-3/2, -1}? See this problem worked out on Moodle for the last week of class in December.
300
Simplify: (8/27)^(-2/3)
What is 9/4?
300
Simplify: (x^2 - 5x - 14)/(4 - x^2)
What is (x-7)/(2-x)?
300
The factored form of 25x^2 - 4.
What is (5x - 2)(5x + 2)? (25x^2 - 4 is a difference of squares.)
300
The reason this equation has no solution: x/(x - 2) + 3 = 2/(x - 2).
What is the restriction says x does not equal 2 and when the problem is solved x = 2 looks like the solution, but that means the denominator is zero, which is not possible.)
300
Solve using the quadratic formula: 2x^2 = 1 - 2x
What is (-1 + or - sqrt 3)/2 ? See this problem worked out on Moodle for the last week of class in December.
400
The domain of x in the expression: (x-2)/(x-6). (Remember, the domain is not the restrictions, it is the set of all values of the variable.)
What is {x|x does not equal 6}?
400
Subtract: x/(x+1) - 2x/(x+2)
What is -(x^2)/((x+1)(x+2))?
400
The factored form of (8x^3 + 27).
What is (2x + 3)(4x^2 - 6x + 9)?
400
Solve: 6(p^2 -1) = 5p
What is (3p + 2)(2p - 3) = 0 or p = -2/3 or 3/2?
400
Solve: square root (2x -1) = x - 2
Remember to square both sides and (x - 2)^2 = x^2 - 4x + 4. What x = 5? (Check to see that 1 does not work.) See this problem worked out on Moodle for the last week of class in December.
500
The |a| when a < 0.
What is -a? (If a = -2, |-2| = -(-2) = 2.)
500
Express each of these as a single polynomial in standard form: (3x - 4)^2 and (3x - 4)(3x + 4)
What are (9x^2 - 24x + 16) and (9x^2 - 16)? (Remember the square of a binomial is always a trinomial.)
500
The factored form of ( 4x^2 - 16x + 15).
What is (2x - 5)(2x - 3)?
500
The original price of a new home which has been reduced by 15% to a new selling price of $125,000.
What is $147,058.82? (Remember the original was 100% of the price--the new price is 15% less or 85% of the original price--an equation would be 1.00x - 0.15x = 125,000--where x is the original price.)
500
Solve: 3 + sqrt(3x + 1) = x
What is {8} ? See this problem worked out on Moodle for the last week of class in December.