C278 College Algebra

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Pass C278 College Algebra with Confidence: Your Curated Set of Practice Exams

Free C278 College Algebra Questions

1. Describe the steps involved in using the addition method to solve a system of equations.

You align the equations, multiply if necessary to match coefficients, and then add or subtract to eliminate a variable.
You convert both equations to standard form before solving.
You graph both equations and identify the point of intersection.
You substitute one variable into the other equation and solve for the remaining variable.

Explanation

The addition method, also known as the elimination method, involves manipulating a system of equations so that adding or subtracting the equations eliminates one of the variables. First, align the equations vertically by corresponding variables. If needed, multiply one or both equations so that the coefficients of one variable are equal (or opposites). Then, add or subtract the equations to eliminate that variable, leaving a single equation with one variable to solve. Once one variable is found, substitute it back into one of the original equations to find the other variable.

2. What is the standard form of a polynomial?

A polynomial that is factored completely.
A polynomial written in descending order of its degree.
A polynomial that contains only positive coefficients.
A polynomial that has no variables.

Explanation

The standard form of a polynomial is when its terms are written in order from the highest degree to the lowest degree. This format makes it easier to identify the degree of the polynomial and to perform operations such as addition, subtraction, or division. The coefficients can be positive or negative; the key feature is the descending order of exponents.

3. What is the highest exponent in the polynomial x³ − 5x² − 9x + 45?

Explanation

The degree of a polynomial is determined by the term with the highest exponent. In the polynomial x³ − 5x² − 9x + 45, the term with the highest exponent is x³, which has an exponent of 3. Therefore, the highest exponent in this polynomial is 3, indicating that it is a cubic polynomial.

4. For the equation 4X + 2 = 10, X equals?

2
12
3
-2

Explanation

To solve 4X + 2 = 10, start by isolating the variable term. Subtract 2 from both sides: 4X = 8. Then, divide both sides by 4 to solve for X: X = 8 ÷ 4 = 2. This gives the value of X that satisfies the equation.

5. Assume that in determining the total cost of a repair job, a 15% shop cost is to be added to the costs of material and labor. For a repair job which cost $200 in materials and $600 in labor, the shop cost is

$90
$120
$60
$30

Explanation

The shop cost is calculated as 15% of the combined cost of materials and labor. The total cost of materials and labor is $200 + $600 = $800. Multiplying $800 by 0.15 gives $120. This represents the additional shop cost to be added to the total repair cost.

6. What is the total cost of the items purchased by the first customer?

$20.00
$15.50
$11.25
$16.75

Explanation

To find the total cost, add the prices of all items purchased by the first customer. For example, if the first customer bought items with costs that sum up to $11.25, then that amount represents the total expenditure. Calculating the sum ensures the correct total for the customer's purchase.

Given the functions m(x) = -8x + 14 and n(x) = -4x + 5, find m(n(-3))

17
3
−147
−122
136

Explanation

Explanation

First compute n(-3). Substitute into n(x) = -4x + 5:

n(-3) = -4(-3) + 5 = 12 + 5 = 17.

Next, substitute this result into m(x).

m(17) = -8(17) + 14.

Compute: -8 . 7 = -136.

Then add 14: -136 + 14 = -122.

Thus, m(n(-3) = -122.

Correct Answer

−122

8. If you have the polynomials (3x⁴ + 7x² − 2) and (5x⁴ − 4x² + 9), what would be the result of (3x⁴ + 7x² − 2) − (5x⁴ − 4x² + 9) in standard form?

2x⁴ + 11x² + 11
−2x⁴ + 11x² − 11
2x⁴ − 11x² + 11
−2x⁴ + 3x² + 7

Explanation

To subtract the polynomials, distribute the negative sign to each term of the second polynomial: (3x⁴ + 7x² − 2) − 5x⁴ + 4x² − 9. Then combine like terms: 3x⁴ − 5x⁴ = −2x⁴, 7x² + 4x² = 11x², and −2 − 9 = −11. Therefore, the resulting polynomial in standard form is −2x⁴ + 11x² − 11.

9. What is the first step in solving the linear equation 5x − (4x − 1) = 2?

Distribute the negative sign
Isolate the variable
Combine like terms
Add 1 to both sides

Explanation

The equation 5x − (4x − 1) = 2 contains parentheses with a negative sign in front. The first step is to distribute the negative sign across the terms inside the parentheses: 5x − 4x + 1 = 2. This simplifies the equation and allows you to combine like terms and isolate the variable in subsequent steps.

10. Describe the process of isolating the variable x in the equation 5 + 4x − 2 = x.

To isolate x, you need to add 2 to both sides of the equation.
To isolate x, you should rewrite the equation in scientific notation.
To isolate x, first combine like terms and then move x to one side of the equation.
To isolate x, you should multiply both sides by 4.

Explanation

To isolate x in the equation 5 + 4x − 2 = x, start by combining like terms on the left-hand side: 5 − 2 + 4x = 3 + 4x. This simplifies the equation to 3 + 4x = x. Next, move x to one side by subtracting x from both sides: 3 + 3x = 0. Finally, subtract 3 from both sides and divide by 3 to solve for x. This process of combining like terms and moving all x terms to one side is the standard method for isolating the variable.

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