2 question

Question 2: Factorize the following quadratic expressions:
1. \(x^2 + 5x + 6\)
2. \(x^2 - 3x - 10\)

Solution:
- To factorize the given quadratic expressions, we need to find two numbers that multiply to the constant term and add up to the coefficient of the middle term.
- For the expression \(x^2 + 5x + 6\), the factors are (x + 2)(x + 3).
- For the expression \(x^2 - 3x - 10\), the factors are (x - 5)(x + 2).

Question 3: Factorize the following quadratic expressions:
1. \(2x^2 + 7x + 3\)
2. \(3x^2 - 5x - 2\)

Solution:
- To factorize the given quadratic expressions, we need to find two numbers that multiply to the product of the coefficient of x^2 term and the constant term and add up to the coefficient of the middle term.
- For the expression \(2x^2 + 7x + 3\), the factors are (2x + 1)(x + 3).
- For the expression \(3x^2 - 5x - 2\), the factors are (3x + 1)(x - 2).

Question 4: Factorize the following quadratic expression:
\(x^2 - 4x - 5\)

Solution:
- To factorize the given quadratic expression, we need to find two numbers that multiply to the constant term and add up to the coefficient of the middle term.
- For the expression \(x^2 - 4x - 5\), the factors are (x - 5)(x + 1).

Question 5: Factorize the following quadratic expression:
\(4x^2 - 4x - 3\)

Solution:
- To factorize the given quadratic expression, we need to find two numbers that multiply to the product of the coefficient of x^2 term and the constant term and add up to the coefficient of the middle term.
- For the expression \(4x^2 - 4x - 3\), the factors are (4x + 3)(x - 1).

Question 6: Factorize the following quadratic expression:
\(6x^2 - 13x + 6\)

Solution:
- To factorize the given quadratic expression, we need to find two numbers that multiply to the product of the coefficient of x^2 term and the constant term and add up to the coefficient of the middle term.
- For the expression \(6x^2 - 13x + 6\), the factors are (3x - 2)(2x - 3).