🧮 algebra

1. **State the problem:** Solve the quadratic equation $$2x^2 - 5x - 12 = 0$$. 2. **Formula used:** The quadratic formula to solve $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \sqrt

1. The problem is to solve a quadratic equation of the form $ax^2 + bx + c = 0$ using the quadratic formula. 2. The quadratic formula is given by:

1. **State the problem:** Solve the quadratic equation $$2x^2 - 5x - 12 = 0$$ completely. 2. **Formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$,

1. **Problem statement:** Given that $x=1$ is a root of the cubic equation $$3x^3 - 8x^2 + 3x + 2 = 0,$$ find the remaining roots using polynomial long division. 2. **Formula and r

1. **State the problem:** We have two lines:

1. **State the problem:** We have two lines:

1. **Problem statement:** Use synthetic division to divide the polynomial $f(x) = 4x^3 - x^2 + 4$ by $x - 2$ and find the quotient and remainder. 2. **Formula and rules:** Syntheti

1. مسئله را بیان می‌کنیم: باید مقدار عبارت $$\sqrt{(x-y)^2} - \sqrt{y^2}$$ را برای شرایط $$x < 0$$ و $$y > 0$$ بیابیم. 2. فرمول‌ها و قواعد مهم:

1. **Problem Statement:** Determine which of the following statements is correct:

1. **State the problem:** Solve the quadratic equation $$w^2 + 12w - 40 = 0$$ and find which of the given options is a solution. 2. **Formula used:** To solve a quadratic equation

1. **State the problem:** Explain how we get the equation $x^2 + 1 = 99x$ from the given $x + \frac{1}{x} = 99$. 2. **Start with the given equation:**

1. **State the problem:** Given that $x + \frac{1}{x} = 99$, find the value of $$\frac{100x}{2x^2 + 102x + 2}$$. 2. **Rewrite the denominator:** Notice the denominator can be facto

1. **Problem:** Find the values of A, B, and C such that $$\frac{2x+1}{(x+1)(x+2)^2} = \frac{A}{x+1} + \frac{B}{x+2} + \frac{C}{(x+2)^2}$$

1. مسئله: تجزیه عبارت داده شده را انجام دهید. 2. برای تجزیه عبارات جبری، باید به دنبال عواملی باشیم که ضرب آن‌ها برابر با عبارت اصلی شود.

1. **State the problem:** Factor the polynomial expression $$6a^6 - 7a^3 b^3 - 8b^6$$. 2. **Identify the structure:** This is a trinomial in terms of $a^3$ and $b^3$. Let $x = a^3$

1. **State the problem:** Solve the quadratic equation $100000000x^2 - 882x = 0$. 2. **Formula and rules:** To solve quadratic equations, we can factorize or use the quadratic form

1. المشكلة: لدينا دالة $x_0 = \exp(-x^2)$ ونريد فهم العلاقة بين $x_0$ و $\exp(-(x-1)^2)$ مع بعض المعادلات المتعلقة بالقيم $x$. 2. نبدأ بفهم المعادلة المعطاة:

1. **State the problem:** We have a table with two days, Monday and Tuesday, showing numbers of flies and mosquitoes. We know Monday has 15 flies and Tuesday has 14 mosquitoes. We

1. مسئله: نمودار تابع $y = x^{3}$ را از انتقال افقی یا عمودی به نمودار $y = 3x^{3}$ تبدیل کنید. 2. فرمول و توضیح: تابع $y = 3x^{3}$ را می‌توان به صورت $y = 3 imes (x^{3})$ نوشت. ا

1. **State the problem:** Factor the quadratic expression $x^2 - 7x + 10$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multip

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl