Matrices and Determinants

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Q1. What is the solution to the equation x^2 + 4x + 4 = 0?

Solution:

Step 1: Factor the equation: (x + 2)(x + 2) = 0. Step 2: Set the factor to zero: x + 2 = 0. Step 3: Solution is x = -2.

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Q2. What is the factored form of the polynomial x^2 - 16?

Solution:

This is a difference of squares: x^2 - 4^2 = (x - 4)(x + 4).

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Q3. What is the value of x in the equation 5x + 2 = 3x + 10?

Solution:

Step 1: Subtract 3x from both sides: 2x + 2 = 10. Step 2: Subtract 2 from both sides: 2x = 8. Step 3: Divide by 2: x = 4.

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Q4. Which of the following is the solution set for the inequality 2x + 3 > 7?

Solution:

Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2.

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Q5. What is the value of x in the equation 4(x - 1) = 2x + 6?

Solution:

Distribute: 4x - 4 = 2x + 6. Subtract 2x from both sides: 2x - 4 = 6. Add 4: 2x = 10. Divide by 2: x = 5.