Factorization Techniques

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Q1. Factor the polynomial: 3x^2 + 12x

Solution:

Factor out the common term 3x: 3x(x + 4).

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Q2. 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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Q3. Solve the inequality: 3x + 4 > 10

Solution:

Subtract 4 from both sides: 3x > 6. Then divide by 3: x > 2.

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Q4. Factor the expression: 4x^2 - 25.

Solution:

The expression 4x^2 - 25 is a difference of squares. It can be factored as (2x - 5)(2x + 5).

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Q5. What are the roots of the equation: x^2 - 4 = 0?

Solution:

Set the equation to zero: x^2 - 4 = 0. Factor as (x - 2)(x + 2) = 0. Thus, the roots are x = -2 and x = 2.

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Q6. 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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Q7. What is the factored form of 2x^2 - 8?

Solution:

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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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. 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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Q10. 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).