College Algebra Study Guide: Polynomials – Standard Form, Classification, Addition & Subtraction

Q1. Write each polynomial in standard form: $x^2 + x + 3$

Background

Topic: Standard Form of Polynomials

This question tests your ability to arrange the terms of a polynomial in descending order of degree.

Key Terms:

• Standard Form: A polynomial is in standard form when its terms are written in order from highest to lowest degree.

• Degree: The highest exponent of the variable in the polynomial.

Step-by-Step Guidance

1. Identify the degree of each term: $x^2$ (degree 2), $x$ (degree 1), $3$ (degree 0).

2. Arrange the terms in descending order of degree: Start with the highest degree term.

3. Write the polynomial in standard form by ordering the terms from highest to lowest degree.

Try solving on your own before revealing the answer!

Q2. Write each polynomial in standard form: $k^3 + 7k - 64 + 2k^2$

Background

Topic: Standard Form of Polynomials

This question asks you to rewrite a polynomial by ordering its terms from highest to lowest degree.

Key Terms:

• Standard Form

• Degree

Step-by-Step Guidance

1. Identify the degree of each term: $k^3$ (degree 3), $2k^2$ (degree 2), $7k$ (degree 1), $-64$ (degree 0).

2. Arrange the terms in descending order of degree.

3. Write the polynomial in standard form.

Try solving on your own before revealing the answer!

Q3. Classify the polynomial $7p^2 + 3p$ by degree and number of terms.

Background

Topic: Classification of Polynomials

This question tests your ability to determine the degree and the number of terms in a polynomial.

Key Terms:

• Degree: The highest exponent of the variable.

• Number of Terms: Count each separate part separated by + or -.

Step-by-Step Guidance

1. Identify the degree of each term: $7p^2$ (degree 2), $3p$ (degree 1).

2. Find the highest degree among the terms.

3. Count the number of terms in the polynomial.

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Q4. Find the sum: $(x^2 - 4x + 3) + (3x^2 - 3x - 5)$

Background

Topic: Adding Polynomials

This question tests your ability to add two polynomials by combining like terms.

Key Terms and Formulas:

• Like Terms: Terms with the same variable and exponent.

• Addition of Polynomials: Combine like terms by adding their coefficients.

Step-by-Step Guidance

1. Write both polynomials in standard form.

2. Group like terms: $x^2$ terms, $x$ terms, and constants.

3. Add the coefficients of like terms.

4. Write the resulting polynomial in standard form.

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Q5. Subtract $(3 - 9m^2 - 2m)$ from $(2m - 3 + 7m^2)$

Background

Topic: Subtracting Polynomials

This question tests your ability to subtract one polynomial from another by combining like terms and distributing the negative sign.

Key Terms and Formulas:

• Subtraction of Polynomials: Distribute the negative sign and combine like terms.

Step-by-Step Guidance

1. Write both polynomials in standard form.

2. Distribute the negative sign to each term in the polynomial being subtracted.

3. Group like terms: $m^2$ terms, $m$ terms, and constants.

4. Add or subtract the coefficients of like terms.

Try solving on your own before revealing the answer!