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Quadratic Factoring Formula:
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Quadratic factoring is the process of expressing a quadratic expression in the form x² + bx + c as a product of two binomials: (x + p)(x + q). This technique is fundamental in algebra for solving quadratic equations and simplifying expressions.
The calculator uses the factoring formula:
Where:
Explanation: The calculator finds two numbers p and q that add up to b and multiply to c, then expresses the quadratic as a product of binomials.
Details: Factoring is essential for solving quadratic equations, finding roots, graphing parabolas, and simplifying algebraic expressions. It's a fundamental skill in algebra and higher mathematics.
Tips: Enter the coefficients b and c from your quadratic expression x² + bx + c. The calculator will attempt to find factors p and q that satisfy the conditions p + q = b and p × q = c.
Q1: What if the quadratic cannot be factored with real numbers?
A: If the discriminant (b² - 4c) is negative, the quadratic cannot be factored using real numbers. The calculator will indicate this.
Q2: Can this calculator handle quadratics with a coefficient other than 1 for x²?
A: This calculator is designed specifically for quadratics in the form x² + bx + c. For ax² + bx + c where a ≠ 1, additional factoring methods are needed.
Q3: What are some common factoring patterns?
A: Common patterns include perfect square trinomials, difference of squares, and sum/difference of cubes, though this calculator focuses on basic quadratic factoring.
Q4: How is factoring related to solving quadratic equations?
A: Once factored, setting each binomial equal to zero gives the solutions to the quadratic equation x² + bx + c = 0.
Q5: Can this calculator handle decimal coefficients?
A: Yes, the calculator can handle decimal inputs for both b and c coefficients.