Final answer:
A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c. Quadratic factorization is a method used to factor quadratic expressions into two binomial expressions. Here's a step-by-step example of how to factor a quadratic expression using quadratic factorization.
Step-by-step explanation:
A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. The solutions to quadratic equations can be found using various methods, such as factoring, completing the square, or using the quadratic formula. One common method is quadratic factorization, which involves factoring the quadratic expression into two binomial expressions. Here's an example:
Question: Factor the quadratic expression 2x^2 + 7x + 3
Step 1: Multiply the coefficient of the leading term (2) and the constant term (3), which gives us 6.
Step 2: Find two numbers that multiply to 6 and add up to the coefficient of the middle term (7). In this case, the numbers are 2 and 3.
Step 3: Rewrite the middle term using the two numbers found in Step 2. The expression becomes 2x^2 + 2x + 3x + 3.
Step 4: Group the terms in pairs. The expression becomes (2x^2 + 2x) + (3x + 3).
Step 5: Factor out the greatest common factor from each pair. The expression becomes 2x(x + 1) + 3(x + 1).
Step 6: Notice that both terms have a common factor of (x + 1). Factor out the common factor. The expression becomes (x + 1)(2x + 3).