Question 1

What is the degree and leading coefficient of the polynomial $$4x^3$$ - $$2x^2 + 7x - 5$?

Accepted Answer

Degree: 3, Leading coefficient: 4

Question 2

Solve the rational equation $$\frac{x}{x+2} = \frac{3}{x+2}$$ for $$x.$$

Accepted Answer

$$x = 3$$

Question 3

Which of the following represents the interval notation for the set $$\{x \mid 1 \u003c x \leq 5\}$$?

Accepted Answer

$$(1,5]$$

Question 4

Solve for $$w in $$the equation $$3(w - 2) = 2w + 4.$$

Accepted Answer

$$w = 10$$

Question 5

Factor the quadratic $$x^2 - 5x + 6$.

Accepted Answer

$$(x - 2)(x - 3)$$

Question 6

Multiply the expressions $$2x \cdot 3y.$$

Accepted Answer

$$6xy$$

Question 7

Fill in the blank to make equivalent rational expressions: $$\frac{2}{x} = \frac{?}{3x}.$$

Accepted Answer

$$6$$

Question 8

Solve for $$b in $$the equation $$a = 2(b + 3).$$

Accepted Answer

$$b = \frac{a}{2} - 3$$

Question 9

Jessica got a prepaid debit card with $$30. She bought ribbon at 0.19$ per yard. After the purchase, she had 25.44$ left. How many yards did she buy?

Accepted Answer

$$16$$ yards

Question 10

Solve for $$y in $$the equation $$(y - 2)(y + 3) = 0.$$

Accepted Answer

$$y = 2 or$$ $$y = -3$$

Question 11

Solve for $$x in $$the equation $$\frac{2x - 3}{4} = 5.$$

Accepted Answer

$$x = 11$$

Question 12

Solve the inequality $$2y - 4 \u003c 10.$$

Accepted Answer

$$y \u003c 7$$

Question 13

Use the quadratic formula to solve $$x^2 - 4x + 1 = 0$.

Accepted Answer

$$x = 2 \pm \sqrt{3}$$

Question 14

A right triangle has legs of length $$7$$ and $$x$$, and hypotenuse $$10. $$What is $$x ($$rounded to the nearest hundredth)?

Accepted Answer

$$x = 7.14$$

Question 15

Factor out the monomial from $$6xy + 12x^2$y.$$

Accepted Answer

$$6x y(1 + 2x)$$

Question 16

Multiply the binomials $$(x + 2)(x + 5).$$

Accepted Answer

$$x^2 + 7x + 10$

Question 17

Simplify $$\frac{a^3$b^2$$}{$$a^2b$$}$.

Accepted Answer

$$ab$$

Question 18

Rewrite $$\frac{1}{x$$^{-2}$$}$$ without a negative exponent.

Accepted Answer

$$x^2$$

Question 19

What is the least common denominator (LCD) of $$\frac{1}{x}$$ and $$\frac{1}{x+1}$$?

Accepted Answer

$$x(x+1)$$

Question 20

Solve the absolute value equation $$|x - 3| = 5.$$

Accepted Answer

$$x = 8 or$$ $$x = -2$$

Unit A Study Guide: Fundamental Concepts of Algebra for Precalculus

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