🧮 algebra

1. **State the problem:** We are given the function $$f(x) = x^3 + ax^2 - ax + 48$$ where $$a$$ is a constant. We know that $$f(-6) = 0$$ and need to find the value of $$a$$. 2. **

1. **State the problem:** We want to divide the polynomial $$2x^4 + 4x^3 - 7x^2 + 2$$ by $$2x^2 + 2x - 7$$ using long division. 2. **Recall the long division formula:** When dividi

1. **State the problem:** Divide the polynomial $$8x^3 + 18x^2 + 19x + 25$$ by the binomial $$2x + 3$$ using long division. 2. **Recall the formula:** When dividing polynomials, th

1. **State the problem:** Divide the polynomial $$6x^3 - 7x^2 + 23x - 7$$ by the binomial $$3x - 2$$ using long division. 2. **Recall the formula:** When dividing polynomials, the

1. **State the problem:** Divide the polynomial $6x^3 - 25x^2 + 8x + 27$ by the binomial $2x - 7$ using long division. 2. **Recall the long division formula:** When dividing $f(x)$

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 2x + 3y = 8 \\ 5x + 6y = 17 \end{cases}$$

1. **State the problem:** Solve the system of equations using substitution: $$y = 3x + 1$$

1. **State the problem:** We need to subtract the complex numbers $$(-7 + 9i)$$ and $$(-7 + 5i)$$. 2. **Recall the rule for subtracting complex numbers:** Subtract the real parts a

1. **State the problem:** We need to simplify the expression $(4 + i) - (2 - 3i) - (3 - 2i)$ and write the result in the form $a + bi$.

1. **State the problem:** Solve the system of linear equations: $$10x - 2y = 44$$

1. **State the problem:** We want to prove that the repeating decimal $0.999999\ldots$ is equal to $1$. 2. **Use a variable to represent the repeating decimal:** Let $x = 0.999999\

1. **State the problem:** We need to solve for $q$ in the equation $$r = -qp$$. 2. **Write the formula and isolate $q$:** The equation is $$r = -qp$$. To solve for $q$, we want to

1. **State the problem:** Solve for $r$ in terms of $s$, $t$, and $u$ given the equation: $$s = t + u + r$$

1. **State the problem:** Solve the linear equation $2x + 3 = 5$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse

1. Muammoni bayon qilamiz: quyidagi ifodani soddalashtiring: $$\frac{2}{m} + \frac{5}{m-3n} - \frac{m-2n}{9n^2-m^2}$$

1. **State the problem:** We need to graph the feasible region for the system of inequalities: $$x + y \leq 5$$

1. **Problem:** Expand and simplify the expression $$(3x + 5)(2x + 7)$$ and find the missing coefficient in $$6x^2 + \square x + 35$$. 2. **Formula:** Use the distributive property

1. **State the problem:** Casey has fixed weekly costs of $200 and variable costs of $2.50 per dessert basket. We want to find her total weekly costs for 40 baskets and determine h

1. **State the problem:** We need to find the product of the matrices $$A = \begin{bmatrix}-9 & -6 \\ -4 & 4\end{bmatrix}$$ and $$B = \begin{bmatrix}4 \\ -5\end{bmatrix}$$ if possi

1. **State the problem:** We need to find the linear function $y = mx + b$ that models the cost $y$ based on the number of people $x$. Given points are $(15,120)$ and $(25,200)$. 2

1. **State the problem:** Find the simplest polynomial function with integer coefficients and positive leading coefficient given zeros at $x=1$, $x=-\frac{1}{2}$, and $x=8$. 2. **R