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Algebra Review
Polynomials
More polynomials
sections 1.1 and 1.2
section 1.2 and 1.4
100
Classify 3pi
What is an irrational number, and real number? Also complex number!!
100
The coefficient and degree for the monomial 2x.
What is 2 and 1?
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 = 7 + (x + 2). Be complete!
What is the commutative 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: (16/9)^(-3/2)
What is 27/64?
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)/(2x+3). (Remember, the domain is not the restrictions, it is the set of all values of the variable.)
What is {x|x does not equal -3/2}?
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.