The expression x^2-10x+24 is equivalent to the factored form (x - 4)(x - 6), and it demonstrates a quadratic equation that can be solved by factoring or using the quadratic formula.
The expression x^2-10x+24 is equivalent to the product of two binomials when factored. We are looking for two numbers that multiply to 24 (the constant term) and add up to -10 (the coefficient of the linear term).
The numbers that fit this criterion are -4 and -6. Therefore, the expression can be factored as:
(x - 4)(x - 6) = x^2 - 10x + 24
This factored form is useful for solving for x when the expression is set to zero, implying a quadratic equation of the form:
ax^2 + bx + c = 0
Using the factors, the solutions to the equation x^2 - 10x + 24 = 0 are x = 4 and x = 6, which can be obtained also by applying the quadratic formula if needed.