Sections 1.1 - 1.8

If u is an algebraic expression and c is a real number such that c>0, then the inequality |u|<c is equivalent to...

-c<u<c

Choose the correct statement below. A. If two factors multiplied together are equal to​ zero, then at least one of the factors must be zero. B. The product of zero and another factor is always zero. C. If the product of two factors is equal to​ zero, then both factors must be equal to 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 at least one of the factors must be zero.

Choose the correct statement below. A. The distance from the number a to 0 on a number line can be represented by the absolute value a number a. B. The opposite value of a number a can be represented by the absolute value of a number a. C. Given |a|​, a is always positive. D. The positive value of a negative number a can be represented by 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 a number a.

If two factors multiplied together are equal to zero, then...

At least one of the factors must be zero.

If u is an algebraic expression and c is a real number such that c>0​, then the inequality |u|<c is equivalent to...? A. u<-c or u>c B. -c<u<c. C. u<-c and u>C. D. -c>u>c.

B. -c<u<c.

Which of the following is NOT a property of inequalities? A. For c<0​, if a<b​, a/c > b/c B. For c>0​, if a<b​, ac<bc. C. For c<0​, if a<b​, a−c>b−c. D. For c<0​, if a<b​, ac>bc.

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

Which of the following is typically NOT one of the three ways to describe the solutions to a linear inequality? A. Write the solution in interval notation. B. Graph the solution on a number line. C. Write the solution in inequality form. D. Write the solution in​ set-builder notation.

C. Write the solution in inequality form.

What is the zero product property?

If AB=0 then A=0 or B=0

True/False? All linear equations and all quadratic equations are polynomial equations.

True

A linear equation is an equation that can be written in the form...

a + bx = c

Quadratic equations can have which kinds of solutions? How are they found?

1) 2 real solutions 2) 2 nonreal solutions 3) a single real solution They are found using the discriminant.

What equation(s) is an example of a polynomial equation?

1) linear equations 2) quadratic equations

|u|<c is equivalent to...

-c<u<c

Choose the correct statement below. A. All linear equations and all quadratic equations are polynomial equations. B. Every linear equation is also a quadratic equation. C. Every quadratic equation is also a linear equation. D. A polynomial equation is either a linear equation or a quadratic equation

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

True/False? It is impossible for an absolute value equation to have no solution.

False

A quadratic equation in one variable is

An equation that can be written in the form ax^2 + bx + c = 0, where a does not equal 0.

How is the quadratic formula derived?

By solving ax^2 + bx + c = 0 where a does not equal 0 for x by completing the square.

Choose the correct statement below. A. The solution to an absolute value equation must always be greater than or equal to zero. B. The solution to an absolute value equation is always positive. C. It is possible for an absolute value equation to have no solution. D. Every absolute value equation has two solutions.

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

If u is an algebraic expression and c is a real number such that c>0​, then the inequality |u|>c is equivalent to...? A. -c<u<c. B. u>-c or u>c. C. u<-c or u>c. D. u<-c or u<c.

C. u<-c or u>c

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. B. -c<u<c. C. u=-c or u=c. D. -u=c.

C. u=-c or u=c

What do you not do to solve ax^3 + bx^2 + cx = 0 ?

DO NOT divide both sides by x.

The absolute value of a number a represents what?

The distance between the number a and 0 on a number line.

What is the square root property?

The solution to the quadratic equation x^2 - c = 0 or equivalently x^2 = c is x = +/- c^1/2 .

Quadratic equations in the form ax^2 + bx + c = 0 are said to be in what form?

The standard form

If u is an algebraic expression and c is a real number such that c>0, then the inequality |u|>c is equivalent to...

u<-c or u>c

|u|>c is equivalent to...

u<-c or u>c

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

u=-c or u=c

|u|=c is equivalent to...

u=-c or u=c