Vector Algebra

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Q1. What is the factored form of the quadratic equation x^2 - 5x + 6?

Solution:

Step 1: Find two numbers that multiply to 6 and add to -5: -2 and -3. Step 2: Write the factors: (x - 2)(x - 3).

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Q2. What is the solution to the equation 3(x + 2) = 2(x + 5)?

Solution:

Step 1: Distribute: 3x + 6 = 2x + 10. Step 2: Subtract 2x from both sides: x + 6 = 10. Step 3: Subtract 6: x = 4.

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Q3. What is the factored form of the expression x^2 + 7x + 10?

Solution:

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Write in factored form: (x + 5)(x + 2).

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Q4. Which of the following is a root of the polynomial x^2 - 4?

Solution:

Step 1: Factor the polynomial: (x - 2)(x + 2). Step 2: Set each factor to zero: x - 2 = 0 or x + 2 = 0. Roots are x = 2 and x = -2.

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Q5. What is the factored form of the polynomial 2x^2 - 8?

Solution:

Step 1: Factor out the common term: 2(x^2 - 4). Step 2: Recognize the difference of squares: 2(x - 4)(x + 4).

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Q6. Which of the following is a solution to the equation 4x + 1 = 17?

Solution:

Step 1: Subtract 1 from both sides: 4x = 16. Step 2: Divide by 4: x = 4.