Factor out the common term 2: 2(x^2 - 4). Then factor x^2 - 4 as (x - 2)(x + 2). Thus, the final factorization is 2(x - 4)(x + 4).
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Q2. Factor the expression: x^2 - 9.
Solution:
The expression x^2 - 9 is a difference of squares. It can be factored as (x - 3)(x + 3).
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Q3. Solve the equation: 5x + 3 = 2x + 12
Solution:
Subtract 2x from both sides: 3x + 3 = 12. Then subtract 3: 3x = 9. Finally, divide by 3: x = 3.
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Q4. Factor the expression: x^2 + 7x + 10.
Solution:
To factor x^2 + 7x + 10, we need two numbers that multiply to 10 and add to 7. The numbers 2 and 5 work. Thus, the factorization is (x + 2)(x + 5).
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Q5. Factor the expression: x^2 - 5x + 6.
Solution:
To factor x^2 - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).
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Q6. Factor the polynomial: 3x^2 + 12x
Solution:
Factor out the common term 3x: 3x(x + 4).
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Q7. Solve the inequality: 3x + 4 > 10
Solution:
Subtract 4 from both sides: 3x > 6. Then divide by 3: x > 2.
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Q8. Factor the expression: x^2 + 6x + 9.
Solution:
The expression x^2 + 6x + 9 is a perfect square trinomial. It factors to (x + 3)(x + 3) or (x + 3)^2.
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Q9. What is the factored form of the expression 4x^2 - 12x?
Solution:
The greatest common factor is 4x. Factoring it out gives us 4x(x - 3).
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Q10. What are the roots of the quadratic equation: x^2 + 6x + 9 = 0?
Solution:
Factor the equation as (x + 3)(x + 3) = 0. Thus, the root is x = -3 (a double root).
