Podcast
Questions and Answers
What is the factored form of the expression $x^2 + 13x + 42$?
What is the factored form of the expression $x^2 + 13x + 42$?
What is the factored form of the expression $9x^2 - 24x + 16$?
What is the factored form of the expression $9x^2 - 24x + 16$?
What are the solutions to the equation $x^2 + 3x - 28 = 0$?
What are the solutions to the equation $x^2 + 3x - 28 = 0$?
4, -7
What are the zeros of the function $f(x) = x^2 + 8x + 16$?
What are the zeros of the function $f(x) = x^2 + 8x + 16$?
Signup and view all the answers
What are the solutions of the equation $(x + 16)^2 = 28$?
What are the solutions of the equation $(x + 16)^2 = 28$?
Signup and view all the answers
Did Anna make a mistake when solving the equation $(x + 4)^2 = 2$?
Did Anna make a mistake when solving the equation $(x + 4)^2 = 2$?
Signup and view all the answers
Solve the quadratic equation $x^2 + 3x - 10 = 0$ by completing the square. What is the solution?
Solve the quadratic equation $x^2 + 3x - 10 = 0$ by completing the square. What is the solution?
Signup and view all the answers
Match each step to the correct method for solving the equation $5x^2 + 8x + 1 = 0$ using the quadratic formula.
Match each step to the correct method for solving the equation $5x^2 + 8x + 1 = 0$ using the quadratic formula.
Signup and view all the answers
Which expression represents the number $3 + √-4$ rewritten in $a + bi$ form?
Which expression represents the number $3 + √-4$ rewritten in $a + bi$ form?
Signup and view all the answers
For the number 18, what is the value of a and b?
For the number 18, what is the value of a and b?
Signup and view all the answers
Did Lupita make a mistake in completing the square to solve $0 = x^2 - 6x + 13$?
Did Lupita make a mistake in completing the square to solve $0 = x^2 - 6x + 13$?
Signup and view all the answers
Did Marcus make a mistake when using the quadratic formula for $0 = x^2 + 5x + 17$?
Did Marcus make a mistake when using the quadratic formula for $0 = x^2 + 5x + 17$?
Signup and view all the answers
Which expression is equivalent to $(2 - √-4) + (1 + √-49)$?
Which expression is equivalent to $(2 - √-4) + (1 + √-49)$?
Signup and view all the answers
Which expression is equivalent to $(2 - 7i) - (-3 + 2i)$?
Which expression is equivalent to $(2 - 7i) - (-3 + 2i)$?
Signup and view all the answers
Given the complex numbers l and m below, what is l - m? l = 3 + 8i, m = 2 - 14i
Given the complex numbers l and m below, what is l - m? l = 3 + 8i, m = 2 - 14i
Signup and view all the answers
Which expression is equivalent to $(2 - 3i) + (2 + 7i)$?
Which expression is equivalent to $(2 - 3i) + (2 + 7i)$?
Signup and view all the answers
Which expression or value is equivalent to $(8 + 2i)(8 - 2i)$?
Which expression or value is equivalent to $(8 + 2i)(8 - 2i)$?
Signup and view all the answers
Which expression is equivalent to $(4 + 6i)(2 + 8i)$?
Which expression is equivalent to $(4 + 6i)(2 + 8i)$?
Signup and view all the answers
Which expression is equivalent to $4i(3 + 9i)$?
Which expression is equivalent to $4i(3 + 9i)$?
Signup and view all the answers
Which expression represents the number $2i^4 - 5i^3 + 3i^2 + √-81$ rewritten in $a + bi$ form?
Which expression represents the number $2i^4 - 5i^3 + 3i^2 + √-81$ rewritten in $a + bi$ form?
Signup and view all the answers
Which expression represents the number $2 + 5i - i(3 - 6i)$ rewritten in $a + bi$ form?
Which expression represents the number $2 + 5i - i(3 - 6i)$ rewritten in $a + bi$ form?
Signup and view all the answers
Which simplifications of the powers of $i$ are correct? Select all that apply.
Which simplifications of the powers of $i$ are correct? Select all that apply.
Signup and view all the answers
Study Notes
Factored Forms
- The expression (x^2 + 13x + 42) factors to ((x + 6)(x + 7)).
- The expression (9x^2 - 24x + 16) factors to ((3x - 4)^2).
Solutions to Equations
- For the equation (x^2 + 3x - 28 = 0), the solutions are (4) and (-7).
- The function (f(x) = x^2 + 8x + 16) has a zero at (-4) only.
- The solutions for ((x + 16)^2 = 28) are (x = -16 ± 2\sqrt{7}).
Completing the Square
- Solving (x^2 + 3x - 10 = 0) by completing the square results in the solutions (2) and (-5).
Quadratic Formula Steps
- The quadratic equation (5x^2 + 8x + 1 = 0) can be solved using the formula, with steps clearly outlined showing each calculation.
Complex Numbers
- The expression (3 + \sqrt{-4}) rewritten in (a + bi) form is (3 + 2i).
- For the number (18), (a = 18) and (b = 0).
- The equivalent expression for ((2 - \sqrt{-4}) + (1 + \sqrt{-49})) is (3 + 5i).
- The equivalent expression for ((2 - 7i) - (-3 + 2i)) is (5 - 9i).
- Calculating (l - m) where (l = 3 + 8i) and (m = 2 - 14i), yields (1 + 22i).
Operations with Complex Numbers
- The expression ( (2 - 3i) + (2 + 7i) ) is equivalent to (4 + 4i).
- The expression ((8 + 2i)(8 - 2i)) simplifies to (68).
- The expression ((4 + 6i)(2 + 8i)) simplifies to (-40 + 44i).
- The expression (4i(3 + 9i)) simplifies to (-36 + 12i).
Simplifications of Powers of i
- The correct simplifications include (i^7 = -i) and (i^{16} = 1).
Final Forms of Complex Expressions
- The expression (2i^4 - 5i^3 + 3i^2 + \sqrt{-81}) in (a + bi) form is (-1 + 14i).
- The expression (2 + 5i - i(3 - 6i)) in (a + bi) form is (-4 + 2i`.
Miscellaneous Notes
- Mistakes can occur when applying procedures; note that Lupita should have added (9) in her solution process, and Marcus incorrectly used (2(5)) instead of (2(1)) in the quadratic formula.
- Ensure to double-check all calculations and logic when solving equations.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards covering key concepts from Algebra 2A, Unit 1. Each card presents essential questions about factoring equations and finding solutions. Perfect for exam preparation!
