Chapter 1

Danielle said that there is no integer that makes the inequality \(|2 x+1|

Joel said that the factors of \(x^{2}+b x+c\) are \((x+d)(x+e)\) if \(d e=c\) and \(d+e=b .\) Do you agree with Joel? Justify your answer.

Explain why the solution set of the equation \(12-|x|=15\) is the empty set.

Explain why the solution of \(|-3 b|=9\) is the same as the solution of \(|3 b|=9\)

Rita said that when the product of three linear factors is greater than zero, all of the factors must be greater than zero or all of the factors must be less than zero. Do you agree with Rita? Explain why or why not.

Ross said that if \((x-a)(x-b)=0\) means that \((x-a)=0\) or \((x-b)=0\) , then \((x-a)(x-b)=2\) means that \((x-a)=2\) or \((x-b)=2 .\) Do you agree with Ross? Explain why or why not.

Melissa said that \((a+3)^{2}=a^{2}+9 .\) Do you agree with Melissa? Justify your answer.

Tina is three years old and knows how to count. Explain how you would show Tina that \(3+2=5 .\)

A binomial is a polynomial with two terms and a trinomial is a polynomial with three terms. Jess said that the sum of a trinomial and binomial is always a trinomial. Do you agree with Jess? Justify your answer.

Marietta factored \(x^{2}+5 x-4\) as \((x+4)(x+1)\) because \(4(1)=4\) and \(4+1=5 .\) Do you agree with Marietta? Explain why or why not.

Are \(-4 x > 12\) and \(x > -3\) equivalent inequalities? Justify your answer.

Explain why the solution set of \(|2 x+4|+7<3\) is the empty set.

Shelley said that if \((x-7)(x-5)<0,\) then \((x-7)\) must be the negative factor and \((x-5)\) must be the positive factor. a. Do you agree with Shelly? Explain why or why not. b. When the product of two factors is negative, is it always possible to tell which is the positive factor and which is the negative factor? Justify your answer.

If \((x-a)(x-b)(x-c)=0,\) is it true that \((x-a)=0,\) or \((x-b)=0\) or \((x-c)=0 ?\) Justify your answer.

Greg said that \(|a-b|=|b-a| .\) Do you agree with Greg? Explain why or why not.

In \(3-12,\) write the sum or difference of the given polynomials in simplest form. $$ (3 y-5)+(2 y-8) $$

In \(3-8,\) write each polynomial as the product of its greatest common monomial factor and a polynomial. $$ 8 x^{2}+12 x $$

In \(3-17,\) solve each equation or inequality. Each solution is an integer. $$ 5 x+4=39 $$

In \(3-14,\) write the solution set of each equation. $$ |x-5|=12 $$

Write the solution set of each inequality if x is an element of the set of integers. \(x^{2}+5 x+6<0\)

Solve and check each of the equations. \(x^{2}-4 x+3=0\)

Perform the indicated operations and write the result in simplest form. 2\(a^{5} b^{2}\left(7 a^{3} b^{2}\right)\)

Find the value of each given expression. \(|6|\)

In \(3-12,\) write the sum or difference of the given polynomials in simplest form. $$ \left(x^{2}+3 x-2\right)+\left(4 x^{2}-2 x+3\right) $$

In \(3-8,\) write each polynomial as the product of its greatest common monomial factor and a polynomial. $$ 6 a^{4}-3 a^{3}+9 a^{2} $$

In \(3-17,\) solve each equation or inequality. Each solution is an integer. $$ 7 x+18=39 $$

In \(3-14,\) write the solution set of each equation. $$ |x+8|=6 $$

Write the solution set of each inequality if x is an element of the set of integers. \(x^{2}+5 x-6>0\)

Solve and check each of the equations. \(x^{2}-7 x+10=0\)

Perform the indicated operations and write the result in simplest form. 6\(c^{2} d\left(-2 c d^{3}\right)\)

Find the value of each given expression. \(|-12|\)

In \(3-8,\) write each polynomial as the product of its greatest common monomial factor and a polynomial. $$ 5 a b^{2}-15 a b+20 a^{2} b $$

In \(3-12,\) write the sum or difference of the given polynomials in simplest form. $$ \left(4 x^{2}-3 x-7\right)+\left(3 x^{2}-2 x+3\right) $$

In \(3-17,\) solve each equation or inequality. Each solution is an integer. $$ 3 b+18=12 $$

In \(3-14,\) write the solution set of each equation. $$ |2 a-5|=7 $$

Write the solution set of each inequality if x is an element of the set of integers. \(x^{2}-3 x+2 \leq 0\)

Solve and check each of the equations. \(x^{2}-5 x-6=0\)

Perform the indicated operations and write the result in simplest form. \(\left(6 x y^{2}\right)^{2}\)

Find the value of each given expression. \(|8-3|\)

In \(3-8,\) write each polynomial as the product of its greatest common monomial factor and a polynomial. $$ x^{3} y^{3}-2 x^{3} y^{2}+x^{2} y^{2} $$

In \(3-12,\) write the sum or difference of the given polynomials in simplest form. $$ \left(-x^{2}+5 x+8\right)+\left(x^{2}-2 x-8\right) $$

In \(3-17,\) solve each equation or inequality. Each solution is an integer. $$ 12-3 y=18 $$

In \(3-14,\) write the solution set of each equation. $$ |5 b-10|=25 $$

Write the solution set of each inequality if x is an element of the set of integers. \(x^{2}-7 x+10>0\)

Solve and check each of the equations. \(x^{2}+6 x+5=0\)

Perform the indicated operations and write the result in simplest form. \(\left(-3 c^{4}\right)^{2}\)

Find the value of each given expression. \(|3-8|\)

In \(3-8,\) write each polynomial as the product of its greatest common monomial factor and a polynomial. $$ 4 a-12 a b+16 a^{2} $$

In \(3-12,\) write the sum or difference of the given polynomials in simplest form. $$ \left(a^{2} b^{2}-a b+5\right)+\left(a^{2} b^{2}+a b-3\right) $$

In \(3-17,\) solve each equation or inequality. Each solution is an integer. $$ 9 a-7=29 $$