Q: Simplify $$\\sqrt{2x} \\sqrt{10x}.$$

$$\\sqrt{20x^2$} = 2x \\sqrt{5}$$

Q: Subtract the square roots: $$6 \\sqrt{45x} - 3x \\sqrt{20x}. $$What is the simplified result?

$$18 \\sqrt{5x} - 6x \\sqrt{5x} = (18 - 6x) \\sqrt{5x}$$

Q: Write an equivalent expression with positive exponents and simplify: $$\\frac{x^5$}{x^8$ y^3$}. $$What is the result and which real numbers must be excluded from the domain?

$$\\frac{1}{x^3$ y^3$}$$; $$x = 0$$ and $$y = 0$$ must be excluded

Q: Find all real numbers that must be excluded from the domain, then multiply and simplify: $$\\frac{(x+3)(x+8)}{6x^2$(x+3)} \\times \\frac{6x(x+1)}{(x+8)(x-3)}.$$

$$\\frac{x+1}{x(x-3)}$$; $$x = 0, x = -3, x = -8, x = 3$$ must be excluded

Question 1

Simplify the expression $$7 - 4[3 - (4x + 5)]. $$What is the result?

Accepted Answer

$$7 - 4[3 - (4x + 5)] = 7 - 4[3 - 4x - 5] = 7 - 4[-2 - 4x] = 7 + 8 + 16x = 15 + 16x$$

Question 2

Rewrite the expression $$|2 - \sqrt{11}|$$ without absolute value bars. What is the result?

Accepted Answer

$$\sqrt{11} - 2$$

Question 3

Factor the perfect square trinomial $$x^2 - 12x + 36$. What is the result?

Accepted Answer

$$(x - 6)^2$

Question 4

Write the following in decimal notation: $$3.827452 \times 10^6$.

Accepted Answer

$$3,827,452$$

Question 5

Write $$-4832.256 in $$scientific notation.

Accepted Answer

$$-4.832256 \times 10^3$

Question 6

Perform the indicated computation and write the answer in scientific notation: $$(9.2 \times 10^5$)(5 \times 10$$^{-4}$$).$$

Accepted Answer

$$4.6 \times 10^2$

Question 7

Simplify $$\sqrt{2x} \sqrt{10x}.$$

Accepted Answer

$$\sqrt{20x^2$} = 2x \sqrt{5}$$

Question 8

Subtract the square roots: $$6 \sqrt{45x} - 3x \sqrt{20x}. $$What is the simplified result?

Accepted Answer

$$18 \sqrt{5x} - 6x \sqrt{5x} = (18 - 6x) \sqrt{5x}$$

Question 9

Factor $$18x^3$$ - $$15x^2. $$What is the result?

Accepted Answer

$$3x^2(6x - 5$$)$$

Question 10

Factor by grouping: $$x^3$$ - $$5x^2 + 3x - 15$. What is the result?

Accepted Answer

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

Question 11

Factor the trinomial $$x^2 + 2x - 24$. What is the result?

Accepted Answer

$$(x + 6)(x - 4)$$

Question 12

Factor $$49 - 25x^2$. What is the result?

Accepted Answer

$$(7 - 5x)(7 + 5x)$$

Question 13

Solve and check: $$3(x - 2) + 2(x + 4) = 22 + x. $$What is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 14

Solve for $$v in $$the equation $$h = ut - 16t^2$. What is v$ in terms of h$, u$, and t$?

Accepted Answer

Question 15

You invested $$10,000 in $$two accounts paying $$2\%$$ and $$9\%$$ annual interest, respectively. If the interest earned for the year was $$410$$, how much was invested at each rate?

Accepted Answer

$$x = 6,000 at$$ $$2\%$$, $$4,000 at$$ $$9\%$$

Question 16

Add the polynomials $$(3x^4$$ + $$5x^2 + 4x$$) + $$(5x^2$$ - $$7x^4$$ + $$8x^2 + 1$$)$$. What is the result?

Accepted Answer

$$-4x^4$$ + $$18x^2 + 4x + 1$

Question 17

Multiply the polynomials and combine like terms: $$(5a + (a - 7a^2$ + 3)). $$What is the result?

Accepted Answer

$$6a - 7a^2$ + 3$$

Question 18

Write an equivalent expression with positive exponents and simplify: $$\frac{x^5$}{x^8$ y^3$}. $$What is the result and which real numbers must be excluded from the domain?

Accepted Answer

$$\frac{1}{x^3$ y^3$}$$; $$x = 0$$ and $$y = 0$$ must be excluded

Question 19

Find all real numbers that must be excluded from the domain, then multiply and simplify: $$\frac{(x+3)(x+8)}{6x^2$(x+3)} \times \frac{6x(x+1)}{(x+8)(x-3)}.$$

Accepted Answer

$$\frac{x+1}{x(x-3)}$$; $$x = 0, x = -3, x = -8, x = 3$$ must be excluded

Precalculus Review: Algebraic Expressions, Factoring, Exponents, and Equations

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