Binomial Theorem (Intro)

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Q1. What is the sum of the roots of the quadratic equation x^2 + 4x + 4 = 0?

Solution:

The sum of the roots is given by -b/a = -4/1 = -4.

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Q2. What is the product of (x + 1)(x + 4)?

Solution:

Step 1: Use the distributive property: x^2 + 4x + x + 4. Step 2: Combine like terms: x^2 + 5x + 4.

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Q3. Which of the following is a solution to the inequality 2x + 3 > 7?

Solution:

Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2. The solution includes all values greater than 2.

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Q4. Which of the following is a solution to the inequality 3x - 4 < 5?

Solution:

Add 4 to both sides: 3x < 9. Then divide by 3: x < 3.

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Q5. What is the result of (x + 2)(x - 3)?

Solution:

Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.

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Q6. Which expression represents the difference of squares for a^2 - b^2?

Solution:

The difference of squares is factored as (a + b)(a - b).

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Q7. What is the value of x in the equation 4x^2 - 12x + 9 = 0?

Solution:

Factor the equation: (2x - 3)(2x - 3) = 0. Thus, x = 3.

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Q8. What is the result of (2x + 3)(x - 1)?

Solution:

Step 1: Use the distributive property: 2x^2 - 2x + 3x - 3. Step 2: Combine like terms: 2x^2 + x - 3.

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Q9. Solve for x: x^2 - 5x + 6 = 0.

Solution:

Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.

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Q10. If 2x + 5 = 3x - 1, what is the value of x?

Solution:

Rearranging gives: 5 + 1 = 3x - 2x, thus x = 6.