Factor Trinomials of the Form $$x^2 + bx + c$$
Unravel quadratic expressions into their factored form. Simply input the coefficients 'b' and 'c' to find the factors (x+p)(x+q).
Factored Form:
Visual Representation
Verification
Expanding the factored form: should result in the original trinomial: . In essence, (x + p)(x + q) = x² + (p + q)x + (p * q) = x² + bx + c.
Understanding Trinomial Factoring (x² + bx + c)
Factoring a trinomial of the form x² + bx + c means rewriting it as a product of two binomials, (x+p)(x+q). To find 'p' and 'q', we need to find two numbers that add up to 'b' (the coefficient of x) and multiply to 'c' (the constant term).
Example: Factor x² + 5x + 6. We need two numbers that add to 5 and multiply to 6. These numbers are 2 and 3. So, x² + 5x + 6 = (x+2)(x+3).
This tool helps you quickly find these factors 'p' and 'q' for given 'b' and 'c' values, simplifying algebraic expressions and solving quadratic equations. It's a fundamental concept in algebra with applications in various mathematical and scientific fields.