Podcast
Questions and Answers
What is the height of the object dropped from a 1500-foot tower after 5 seconds?
What is the height of the object dropped from a 1500-foot tower after 5 seconds?
760 feet
What are the solutions to the equation $x^2 + 8x + 15 = 0$?
What are the solutions to the equation $x^2 + 8x + 15 = 0$?
x = -3 or x = -5
What is the result of performing the operation $(3x^2 + 5) + (7x - 2)$?
What is the result of performing the operation $(3x^2 + 5) + (7x - 2)$?
3x^2 + 7x + 3
What is the simplified result of dividing $(45p^8 + 36p^4) / 9p^2$?
What is the simplified result of dividing $(45p^8 + 36p^4) / 9p^2$?
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What is the simplified form of $m^3 m^{-2} m^{-4}$ using positive exponents only?
What is the simplified form of $m^3 m^{-2} m^{-4}$ using positive exponents only?
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What factored form do you get for $x^2 + 6x - 7$?
What factored form do you get for $x^2 + 6x - 7$?
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What is the factored form of $6x^2 + 11x - 10$?
What is the factored form of $6x^2 + 11x - 10$?
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What is the factored form of the polynomial $9x^2 - 25$?
What is the factored form of the polynomial $9x^2 - 25$?
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What is the simplified result of multiplying the polynomials (2x + 3)(4x - 5)?
What is the simplified result of multiplying the polynomials (2x + 3)(4x - 5)?
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When simplifying the expression (8y^2)(-2y^4), what is the resulting expression?
When simplifying the expression (8y^2)(-2y^4), what is the resulting expression?
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What do you get when you subtract the polynomials (9x^3 + 5) - (4x^3 - 2)?
What do you get when you subtract the polynomials (9x^3 + 5) - (4x^3 - 2)?
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Factor the trinomial x^2 + 6x - 7 completely.
Factor the trinomial x^2 + 6x - 7 completely.
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What is the solution to the equation x(4x + 3) = 27?
What is the solution to the equation x(4x + 3) = 27?
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What is the result of multiplying the polynomials (x + 2)(x - 3)?
What is the result of multiplying the polynomials (x + 2)(x - 3)?
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How will you factor the polynomial 9x^2 - 25?
How will you factor the polynomial 9x^2 - 25?
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When will the object thrown from a 50-foot building hit the ground given the equation h = -16t^2 + 32t + 50?
When will the object thrown from a 50-foot building hit the ground given the equation h = -16t^2 + 32t + 50?
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Study Notes
Multiplying Polynomials
- (2x+3)(4x−5) = 8x² - 7x - 15
- (8y²)(-2y⁴) = -16y⁶
Subtracting Polynomials
- (9x³ + 5) - (4x³ - 2) = 5x³ + 7
Factoring Polynomials
- 6x² + 11x - 10 = (3x - 2)(2x + 5)
- x² + 6x - 7 = (x + 7)(x - 1)
Dividing Polynomials
- (5x³ - 3x² + 4)/(x - 2) = 5x² + 7x + 14 with a remainder of 32
- (6x³ + 11x² + 5)/(2x + 1) = 3x² + 4x + 1 with a remainder of 4
Solving Quadratic Equations
- x(4x+3) = 27 has solutions x = 3 or x = -9/4
- x² + 8x + 15 = 0 has solutions x = -3 or x = -5
Simplifying Expressions
- (3x² + 5) + (7x - 2) = 3x² + 7x + 3
- m³ * m⁻² * m⁻⁴ = m⁹
Factoring by Grouping
- 2x + 8 + 3xy + 12y = (2 + 3y)(x + 4)
Quadratic Equations with Real-World Applications
- An object thrown upward from a building with a height function of h = -16t² + 32t + 50 will hit the ground at t = 3 seconds.
- An object dropped from a tower with a height function of h = -16t² + 1500 will have a height of 760 feet at t = 5 seconds.
Simplifying with Exponents
- (45p⁸ + 36p⁴)/9p² = 5p⁶ + 4p²
- m³/m⁻²m⁻⁴ = m⁹
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Description
This quiz covers various aspects of algebra, focusing on operations with polynomials including multiplication, subtraction, factoring, and division. Additionally, it explores solving quadratic equations and their applications in real-world scenarios. Engage your skills in manipulating algebraic expressions and understanding their roots.
