Questions and Answers
Which of the following algebraic properties was applied to the expression $a + (b + c) = (a + b) + c$?
Which of the following simplifies to -1?
What is the k value for the polynomial $x^3 - 7x^2 + 17x - 15$ if a factor is $x - 3$?
3
Given the equation $x^{1/2} + 2x^{1/4} + 1$, what is the value that u would represent when substituted into the equation?
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Which of the following is the correct sum for $3ig( ext{square root}8ig) - 2ig( ext{square root}32ig)$?
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Which of the following correctly simplifies $4x$?
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Which of the following values is a zero for the polynomial $x^3 + 4x^2 - 17x - 60$?
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Which of the following correctly sets up the synthetic division for $x^4 + 2x^3 - 8x + 11$ divided by $x-5$?
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Which of the following correctly represents the solution for the polynomial $\frac{x-3}{x+5} \geq 0$?
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Study Notes
Algebraic Properties
- Associative property applies to the expression ( a + (b + c) = (a + b) + c ), indicating that grouping does not affect the sum.
Complex Numbers
- The square of ( i ) (the imaginary unit) simplifies to -1, essential in complex number calculations.
Polynomial Functions
- To find the ( k ) value in the polynomial ( x^3 - 7x^2 + 17x - 15 ) with ( x-3 ) as a factor, substitute ( x = 3 ) into the polynomial.
Substitution and Exponents
- If ( u = x^{1/4} ), substituting ( u ) into the equation ( x^{1/2} + 2x^{1/4} + 1 ) helps in simplifying calculations using the common denominator.
Radical Expressions
- Simplifying ( 3\sqrt{8} - 2\sqrt{32} ) leads to understanding how to combine radical terms and find efficient equivalent forms.
Simplification of Expressions
- For terms like ( 4x ), ensure the expression is simplified correctly to understand polynomial operations.
Polynomial Zeros
- The value ( 4 ) is identified as a zero of the polynomial ( x^3 + 4x^2 - 17x - 60 ), indicating a root of the equation.
Synthetic Division Setup
- Synthetic division set up for dividing ( x^4 + 2x^3 - 8x + 11 ) by ( x - 5 ) requires arranging coefficients properly for calculations.
Inequalities and Intervals
- The solution set for the inequality ( \frac{x-3}{x+5} \geq 0 ) is represented as ( (-\infty, -5) ) and ( [3, \infty) ), showing where the expression holds true.
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Test your knowledge with these flashcards covering key concepts from the Abeka Algebra II curriculum. Each card presents a definition or question about algebraic properties, simplifications, and polynomial functions. Perfect for reviewing before your quarter exam!
