Algebra 2A - Unit 1: Exam Flashcards

Questions and Answers

What is the factored form of the expression $x^2 + 13x + 42$?

(x + 5)(x + 8)

(x + 3)(x + 10)

(x + 6)(x + 7) (correct)

(x - 6)(x - 7)

What is the factored form of the expression $9x^2 - 24x + 16$?

(3x - 4)(3x - 4)

(3x + 4)(3x + 4)

(9x - 16)(x + 1)

(3x - 4)^2 (correct)

What are the solutions to the equation $x^2 + 3x - 28 = 0$?

4, -7

What are the zeros of the function $f(x) = x^2 + 8x + 16$?

-4 only Signup and view all the answers

What are the solutions of the equation $(x + 16)^2 = 28$?

x = -16 ± 2√7 Signup and view all the answers

Did Anna make a mistake when solving the equation $(x + 4)^2 = 2$?

False Signup and view all the answers

Solve the quadratic equation $x^2 + 3x - 10 = 0$ by completing the square. What is the solution?

2, -5 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.

Step 1 = x = -8 ± √$8^2 - 4(5)(1)$ / 2(5) Step 2 = x = -8 ± √$64 - 20$ / 10 Step 3 = x = -8 ± √$44$ / 10 Step 4 = x = -8 ± $2√11$ / 10 Step 5 = x = -4 ± $√11$ / 5 Signup and view all the answers

Which expression represents the number $3 + √-4$ rewritten in $a + bi$ form?

3 + 2i Signup and view all the answers

For the number 18, what is the value of a and b?

a = 18 and b = 0 Signup and view all the answers

Did Lupita make a mistake in completing the square to solve $0 = x^2 - 6x + 13$?

True Signup and view all the answers

Did Marcus make a mistake when using the quadratic formula for $0 = x^2 + 5x + 17$?

True Signup and view all the answers

Which expression is equivalent to $(2 - √-4) + (1 + √-49)$?

3 + 5i Signup and view all the answers

Which expression is equivalent to $(2 - 7i) - (-3 + 2i)$?

5 - 9i Signup and view all the answers

Given the complex numbers l and m below, what is l - m? l = 3 + 8i, m = 2 - 14i

1 + 22i Signup and view all the answers

Which expression is equivalent to $(2 - 3i) + (2 + 7i)$?

4 + 4i Signup and view all the answers

Which expression or value is equivalent to $(8 + 2i)(8 - 2i)$?

68 Signup and view all the answers

Which expression is equivalent to $(4 + 6i)(2 + 8i)$?

-40 + 44i Signup and view all the answers

Which expression is equivalent to $4i(3 + 9i)$?

-36 + 12i Signup and view all the answers

Which expression represents the number $2i^4 - 5i^3 + 3i^2 + √-81$ rewritten in $a + bi$ form?

-1 + 14i Signup and view all the answers

Which expression represents the number $2 + 5i - i(3 - 6i)$ rewritten in $a + bi$ form?

-4 + 2i Signup and view all the answers

Which simplifications of the powers of $i$ are correct? Select all that apply.

$i^7 = -i$ 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.

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