🧮 algebra

1. **State the problem:** Factor the polynomial $$6m^3 + 5mn + 6m^2 + 5n$$ by grouping. 2. **Group terms:** Group the polynomial into two pairs:

1. **State the problem:** Factor the polynomial $$4x + 16 + xy + 4y$$ by grouping. 2. **Group terms:** Group the polynomial into two pairs:

1. **State the problem:** Determine if the relation given by the arrow diagram is a function. 2. **Recall the definition of a function:** A relation is a function if every input (d

1. **State the problem:** Factor the polynomial $$-12a^4 + 9a^3 - 3a^2$$ completely, including factoring out a negative number or a GCF with a negative coefficient. 2. **Identify t

1. **Problem a:** Find the point of intersection of the lines $y=2x-1$ and $y=-x+8$. 2. To find the intersection, set the two expressions for $y$ equal:

1. **State the problem:** Factor the polynomial $$-7x - 35$$ by factoring out the greatest common factor (GCF) with a negative coefficient. 2. **Identify the GCF:** The terms are $

1. **State the problem:** Simplify the expression $z(y + 7) - 8(y + 7)$. 2. **Identify the common factor:** Both terms contain the factor $(y + 7)$.

1. **State the problem:** We are given four data points that suggest an exponential decay pattern: 16,510.34, 13,266.81, 10,778.49, and 8,774.27. 2. **Identify the exponential func

1. **State the problem:** Find the solution to the system of linear equations: $$y = -2x - 9$$

1. **State the problem:** Factor the polynomial $$\frac{1}{6}x^9 + \frac{5}{6}x^8 - \frac{7}{6}x^7 + \frac{1}{6}x.$$ 2. **Identify common factors:** Each term has a factor of $$\fr

1. The problem is to find the common ratio (base) of an exponential function that models the data points for money in an account: $144.07$, $374.53$, $605.68$, and $834.53$. 2. An

1. The problem is to simplify the expression $ (7y)^{\frac{1}{3}} $ using the power of a product property. 2. The power of a product property states that $ (ab)^n = a^n b^n $ for a

1. The problem asks to simplify the expression $\left(9^{\frac{1}{4}}\right)^{\frac{7}{2}}$ using the power of a power property. 2. The power of a power property states that $\left

1. **Problem Statement:** Solve the system of linear equations: $$\begin{cases} x + 3y = 12 \\ 2x + y = 6 \end{cases}$$

1. **State the problem:** Factor out the greatest common factor (GCF) from the polynomial $$a^7 b^6 - a^3 b^2 + a^2 b^5 - a^2 b^2$$. 2. **Identify the GCF:**

1. **State the problem:** Factor the expression $25x - 75y + 25$. 2. **Identify the greatest common factor (GCF):** The coefficients are 25, -75, and 25. The GCF of 25, 75, and 25

1. **State the problem:** Factor out the greatest common factor (GCF) from the polynomial $$x^7 + 9x^6$$. 2. **Identify the GCF:** The terms are $$x^7$$ and $$9x^6$$. The GCF of th

1. **State the problem:** Factor out the greatest common factor (GCF) from the polynomial $9x + 18$. 2. **Identify the GCF:** The terms are $9x$ and $18$. The GCF of $9$ and $18$ i

1. **State the problem:** Factor out the greatest common factor (GCF) from the polynomial $9x + 18$. 2. **Identify the GCF:** The terms are $9x$ and $18$. The GCF of $9$ and $18$ i

1. **State the problem:** Find the greatest common factor (GCF) of the terms $63x^2y$, $9x^3y^4$, and $90x^3y$. 2. **Recall the formula and rules:** The GCF is found by taking the

1. **State the problem:** Find the greatest common factor (GCF) of the terms $91x$ and $143$. 2. **Prime factorization:**