Q1. Factor the trinomial:

Background

Topic: Factoring Quadratic Trinomials

This question tests your ability to factor a quadratic expression of the form .

Key Terms and Formulas:

• Quadratic trinomial: An expression with three terms, usually .

• Factoring: Writing the expression as a product of two binomials.

Step-by-Step Guidance

1. Identify , , and in the trinomial .

2. To factor, look for two numbers that multiply to and add to .

3. List pairs of integers whose product is and check which pair sums to $13$.

4. Once you find the correct pair, rewrite the middle term as a sum of those two numbers times .

5. Group the terms and factor by grouping.

Try solving on your own before revealing the answer!

Q2. Factor the trinomial:

Background

Topic: Factoring Quadratic Trinomials with Two Variables

This question tests your ability to factor a quadratic trinomial involving and .

Key Terms and Formulas:

• Quadratic trinomial:

• Factoring: Expressing as a product of two binomials.

Step-by-Step Guidance

1. Identify , , in the trinomial .

2. Find two numbers that multiply to and add to .

3. List pairs of integers whose product is $10-7$.

4. Rewrite as a sum of two terms using the pair found.

5. Factor by grouping.

Try solving on your own before revealing the answer!

Q3. Find the product:

Background

Topic: Multiplying Polynomials

This question tests your ability to multiply a binomial and a trinomial.

Key Terms and Formulas:

• Distributive property:

• Polynomial multiplication: Multiply each term in the first polynomial by each term in the second.

Step-by-Step Guidance

1. Write out .

2. Multiply by each term in : and .

3. Multiply by each term in : and .

4. Combine all the resulting terms.

5. Combine like terms where possible.

Try solving on your own before revealing the answer!

Q4. Solve the equation by the square root property:

Background

Topic: Solving Quadratic Equations Using Square Root Property

This question tests your ability to solve a quadratic equation by isolating and taking the square root.

Key Terms and Formulas:

• Square root property: If , then .

Step-by-Step Guidance

1. Start with .

2. Divide both sides by $2x^2$.

3. Apply the square root property: .

4. Simplify the square root as much as possible.

Try solving on your own before revealing the answer!

Q5. Solve the equation using the quadratic formula:

Background

Topic: Quadratic Formula

This question tests your ability to solve a quadratic equation using the quadratic formula.

Key Terms and Formulas:

• Quadratic formula:

• For , identify , , and .

Step-by-Step Guidance

1. Identify , , .

2. Plug these values into the quadratic formula.

3. Calculate the discriminant: .

4. Set up the formula for using the calculated discriminant.

Try solving on your own before revealing the answer!