Chapter 1.1-1.4 homework answers

Which of the following is true? a. All linear equations and all quadratic equations are polynomial equations. b. A polynomial equation is either a linear equation or a quadratic equation. c. Every linear equation is also a quadratic equation. d. Every quadratic equation is also a linear equation.

a. All linear equations and all quadratic equations are polynomial equations.

Which of the following best describes the zero product property? a. If two factors multiplied together are equal to zero, then a least one of the factors must be zero. b. If the product of two factors is equal to zero, then both factors must be equal to zero. c. The product of zero and another factor is always zero. d. If two nonzero factors are multiplied together, then the product must also be nonzero.

a. If two factors multiplied together are equal to zero, then a least one of the factors must be zero.

Which of the following statements is true? a. It is possible for an absolute value equation to have no solution. b. Every absolute value equation has two solutions. c. The solution to an absolute value equation must always be greater than or equal to zero. d. The solution to an absolute value equation is always positive.

a. It is possible for an absolute value equation to have no solution.

Which of the following statements describes the absolute value of a number a? a. The distance from the number a to 0 on a number line can be represented by the absolute value of a number a. b. The positive value of a negative number a can be represented by the absolute value of a number a. c. The opposite value of a number a can be represented by the absolute value of a number a. d. Given |a|, a is always positive.

a. The distance from the number a to 0 on a number line can be represented by the absolute value of a number a.

Which of the following statements is not true? a. The solutions to quadratic equations are always real numbers. b. In order for the equation ax^2+bx+c=0 to be considered a quadratic equation, the coefficient a must be nonzero. c. The quadratic formula can be used to solve every quadratic equation. d. The method of completing the square can be used to solve every quadratic equation.

a. The solutions to quadratic equations are always real numbers.

Suppose that you are solving a quadratic equation and realize that the discriminant is equal to 7. Which of the following statements best describes the solutions to this quadratic equation? a. There must be two real solutions. b. There must be two non real solutions. c. There will be no solutions to this quadratic equation. d. There must be exactly one real solution.

a. There must be two real solutions.

Which of the following statements is not true concerning the equation x^2-c=0 for c>0? a. This equation is not considered to be a quadratic equation because it is not of the form ax^2+bx+c=0 b. The left-hand side of this equation is called a difference of two squares. c. A quadratic equation in this form can always be solved using the square root property. d. A quadratic equation in this form can always be solved by factoring.

a. This equation is not considered to be a quadratic equation because it is not of the form ax^2+bx+c=0

If u is an algebraic expression and c is a real number such that c>0, then the equation |u|>c is equivalent to a. u>-c or u>c. b. u<-c or u>c. c. u<-c or u<c. d. -c<u<c.

b. u<-c or u>c.

Which of the following equations is not disguised quadratic equation? a. x^(2/3)-9x^(1/3)+8=0 b. x^5-x^3-6=0 c. 3x^(-2)-5x^(-1)-2=0 d. 2x^4-11x^2+12=0

b. x^5-x^3-6=0

If u is an algebraic expression and c is a real number such that c>0, then the equation |u|<c is equivalent to a. u<-c or u>c. b. u<-c and u>c. c. -c<u<c. d. -c>u>c.

c. -c<u<c.

Which of the following statements best defines the term "extraneous solution"? a. An extraneous solution is an irrational solution to an algebraic equation. b. An extraneous solution is an approximate solution to an algebraic equation. c. An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation. d. An extraneous solution is a solution to a linear equation that contains fractions.

c. An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.

Which of the following is not a valid strategy when solving a polynomial equation of the form ax^3+bx^2=cx? a. Subtract cx from both sides. b. Set the equation equal to zero and factor out an x. c. Divide the equation by x. d. subtract ax^3 and bx^2 from both sides.

c. Divide the equation by x.

Which of the following statements is true about rational equations? a. rational equations always have no solution. b. a rational equation can never lead to a linear equation. c. it is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions. d. when solving a rational equation, it is never a good idea to multiply both sides of the equation by the least common denominator.

c. it is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions.

Which of the following is a rational equation? a. 4-2(x-1)=x+3 b. 1/2 x- 1/3=4-x c. 0.7x-3=0.09(x-5) d. 6/x -1=4/(x-2)

d. 6/x -1=4/(x-2)

Which of the following statements best defines the term "algebraic expression"? a. An algebraic expression consists of two algebraic terms separated by an operating symbol such as - or +. b. An algebraic expression is equivalent to an algebraic equation. c. An algebraic expression consists of one algebraic term. d. An algebraic expression consists of one or more terms that may include variables, constants, and operating symbols such as - and +.

d. An algebraic expression consists of one or more terms that may include variables, constants, and operating symbols such as - and +.

Which of the following is not a property of inequalities? a. For c>0, if a<b, ac<bc. b. For c<0, if a<b, (a/c)>(b/c) c. For c<0, if a<b, ac>bc. d. For c<0, if a<b, a-c>b-c.

d. For c<0, if a<b, a-c>b-c.

Which of the following statements is true about linear equations of the form ax+b=c? a. The constants a, b, and c must be real numbers with the constant always a positive. b. The constants a, b, and c can never be decimals. c. The constants a, b, and c can never be fractions. d. The constants a, b, and c must be real numbers with the constant a never equal to zero.

d. The constants a, b, and c must be real numbers with the constant a never equal to zero.

Which of the following statements best describes how to derive the quadratic formula? a. The quadratic formula can only be derived using calculus. b. The quadratic formula can be derived by solving the equation ax^2+bx+c=0, a is not = 0, for x using the zero product property. c. The quadratic formula can be derived by solving the equation ax^2+bx+c=0, a is not = 0, for x by factoring. d. The quadratic formula can be derived by solving the equation ax^2+bx+c=0, a is not = 0, for x using the method of completing the square.

d. The quadratic formula can be derived by solving the equation ax^2+bx+c=0, a is not = 0, for x using the method of completing the square.

Which of the following is typically not one of the three ways to describe the solutions to a linear equality? a. Write the solution in interval notation. b. Graph the solution on a number line. c. Write the solution in set-builder notation. d. Write the solution in inequality form.

d. Write the solution in inequality form.

If u is an algebraic expression and c is a real number such that c>0, then the equation |u|=c is equivalent to a. the equation -u=c. b. the equation u=-c c. the equations u=-c and u=c. d. the equations u=-c or u=c.

d. the equations u=-c or u=c.