Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{2} - 5x + 6 = (x - 2)(x - 3) \)
Solution
Разложим многочлен на множители.
Найдем два числа, произведение которых равно 6, а сумма — -5. Подходящие числа: -2 и -3, так как
(-2) · (-3) = 6
и
(-2) + (-3) = -5.
Следовательно, факторизация выглядит следующим образом:
x² - 5x + 6 = (x - 2)(x - 3).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
Did you know that the polynomial \( x^2 - 5x + 6 \) can be factored into \( (x-2)(x-3) \)? This means its roots, or the x-values that make the equation true, are \( x = 2 \) and \( x = 3 \). It's a handy way to solve quadratics quickly, and helps paint a picture of the function! In real-world applications, such quadratic equations often model trajectory paths, such as the arc of a thrown ball. By setting \( x^{2}-5x+6 = 0 \), you can find where the ball hits the ground (the x-axis), which is essential for sports, engineering designs, and physics experiments alike!
