Test 1 Review - Answer Key Flashcards

A collection of vocabulary-style flashcards providing terms and step-by-step solutions for algebraic equations, word problems, complex numbers, polynomial operations, and factoring expressions from the Test 1 Review.

Solution to $6a - 2 = 64$

$$a = 11$$

Solution to $-2(y+4) = 18 - 6y$

$$y = \frac{13}{2}$$

Solution to $\frac{3}{2}n - \frac{8}{3} = -\frac{29}{12}$

$n = \frac{1}{6}$ (found using LCD of $12$)

Solution to $-7x + 4(2x) + 8 = -3(x-3) - 1$

All real numbers (yields the true identity $8 = 8$)

Rectangular Dog Pen Dimensions

Width $W = 9\,\text{ft}$, Length $L = 15\,\text{ft}$ (given perimeter $P = 48\,\text{ft}$ and length $6\,\text{ft}$ more than width)

Rectangular Carpet Dimensions

Width $W = 40\,\text{in}$, Length $L = 75\,\text{in}$ (given perimeter $P = 230\,\text{in}$ and length $5\,\text{in}$ less than twice the width)

Simplified form of $(7x^{-4}y^5)^3$

$$\frac{343y^{15}}{x^{12}}$$

Simplified form of $2x^5(-9x^6)$

$$-18x^{11}$$

Simplified complex number $-2 + 3i + 4i - 8$

$$-10 + 7i$$

Simplified complex number $(3+5i) - (6-9i)$

$$-3 + 14i$$

Simplified complex product $(6+5i)(4-3i)$

$$39 + 2i$$

Simplified complex square $(8-3i)^2$

$$55 - 48i$$

Polynomial sum $(8x^2 - 5x + 7) + (3x^2 - 10x - 9)$

$$11x^2 - 15x - 2$$

Polynomial difference $(12x^2 - 10x - 15) - (7x^2 + x - 8)$

$$5x^2 - 11x - 7$$

Polynomial product $(2x+1)(3x-4)$

$$6x^2 - 5x - 4$$

Polynomial square $(3-x)^2$

$$x^2 - 6x + 9$$

Polynomial product $(3x-5)(3x+5)$

$$9x^2 - 25$$

Factored form by grouping of $4x^2 - 20x + x - 5$

$$(4x+1)(x-5)$$

Factored form by grouping of $8x^3 - 20x^2 + 6x - 15$

$$(4x^2+3)(2x-5)$$

Factored form of $x^2 - 5x - 24$

$$(x-8)(x+3)$$

Factored form of $-x^2 + 2x + 15$

$$-1(x-5)(x+3)$$

Factored form of $2x^2 + 26x + 80$

$$2(x+8)(x+5)$$

Factored form of $8x^2 + 33x + 4$

$$(8x+1)(x+4)$$

Factored form of $5x^2 + 7x - 6$

$$(5x-3)(x+2)$$

Factored form of $9x^2 - 25$

$$(3x+5)(3x-5)$$