Factorization Techniques

⏱ Time: 0s

Q1. What is the solution to the inequality 3x - 7 < 2?

Solution:

To solve 3x - 7 < 2, add 7 to both sides: 3x < 9. Then divide by 3: x < 3.

⏱ Time: 0s

Q2. 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).

⏱ Time: 0s

Q3. 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).

⏱ Time: 0s

Q4. 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.

⏱ Time: 0s

Q5. Factor the polynomial: 3x^2 + 12x

Solution:

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

⏱ Time: 0s

Q6. 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).

⏱ Time: 0s

Q7. 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.

⏱ Time: 0s

Q8. 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).

⏱ Time: 0s

Q9. 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).

⏱ Time: 0s

Q10. Factor the expression: 2x^2 + 8x.

Solution:

First, we can factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).