🧮 algebra

1. **State the problem:** We want to find the value of $w$ such that when the polynomial $$f(x) = 5x^4 + 9x^3 - 7x^2 + wx - 3$$ is divided by $x + 2$, the remainder is 3. 2. **Reca

1. **State the problem:** Find all real zeros of the polynomial $$f(x) = 3x^3 + 14x^2 + 7x - 4$$ given that one zero is $x = -4$. 2. **Recall the Factor Theorem:** If $x = a$ is a

1. **State the problem:** We need to write a polynomial in factored form given the roots $-6$, $-2$, and $-4$. 2. **Recall the Factor Theorem:** If $r$ is a root of a polynomial, t

1. **State the problem:** We need to find the remainder when the polynomial $$4x^2 - 3x - 7$$ is divided by $$x + 7$$. 2. **Recall the Remainder Theorem:** The remainder when a pol

1. The problem is to simplify the expression $x2-3$. 2. First, recognize that $x2$ means $x \times 2$, so the expression can be rewritten as $2x - 3$.

1. **State the problem:** We need to find the slopes of two lines given two points on each line and then determine the relationship between the lines (parallel, perpendicular, or n

1. **State the problem:** Given $x=3$ and $y=4$, find the value of $x+y$. 2. **Formula used:** The sum of two numbers $x$ and $y$ is given by:

1. The problem is to find the sum of $x$ and $y$ given $x=9$ and $y=8$. 2. The formula for the sum of two numbers is $x + y$.

1. **State the problem:** Solve the equation $-9p - 10 = -64$ for $p$. 2. **Add 10 to both sides:**

1. **State the problem:** We are given the linear equation $$y = -3x - 3$$ and want to understand its properties. 2. **Formula and rules:** This is a linear equation in slope-inter

1. **State the problem:** We need to graph the line given by the equation $$y = \frac{1}{3} x - 3$$. 2. **Formula and explanation:** This is a linear equation in slope-intercept fo

1. **Stating the problem:** We have two red strips on a number line that are equal in length. 2. **Given:**

1. **Understanding the question:** You asked why we multiply by $5$ in the previous problem. 2. **Context of multiplication:** Multiplying by $5$ means we are scaling or repeating

1. **State the problem:** We want to understand how to interpret the shaded columns on a 10 x 10 decimal grid where the entire grid represents one whole. 2. **Understand the grid:*

1. إذا كان $x^2 = 2$ فإن $x = \sqrt{2}$؟ - هذا خطأ لأن المعادلة $x^2 = 2$ لها حلان: $x = \sqrt{2}$ و $x = -\sqrt{2}$.

1. **Statement:** If $x^2=2$ then $x=\sqrt{2}$. **Explanation:** The equation $x^2=2$ has two solutions: $x=\sqrt{2}$ and $x=-\sqrt{2}$. So the statement is **False** because it ig

1. **Probleemstelling:** We willen de snelheid $x$ vinden waarbij de totale kosten van het vervoer van 400 km minimaal zijn.

1. **State the problem:** Simplify the expression $$(5x^2y^4)^3$$. 2. **Recall the power of a product rule:** $$(abc)^n = a^n b^n c^n$$.

1. The problem asks for the slope and y-intercept of a line. 2. The slope-intercept form of a line is $$y = mx + b$$ where $$m$$ is slope and $$b$$ is y-intercept.

1. **State the problem:** Find the slope and y-intercept of the line given by $$25x - 20y = 100$$. 2. **Rewrite the equation in slope-intercept form $$y = mx + b$$:**

1. **State the problem:** We have the equation $$5f + 2p = 90$$ and want to solve for $p$. 2. **Isolate $p$:** Subtract $5f$ from both sides: