🧮 algebra

1. **State the problem:** Factor the quadratic expression $$9x^2 + 17x - 2$$ into the product of two binomials. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c

1. **State the problem:** Solve the quadratic equation $$2x^2+7x+4=8$$ using the quadratic formula. 2. **Rewrite the equation in standard form:** Move all terms to one side:

1. **State the problem:** Factor the quadratic expression $$x^2 - 10x + 16$$ into the product of two binomials. 2. **Recall the factoring formula:** For a quadratic expression $$x^

1. **State the problem:** We need to rewrite the quadratic function $y = 3x^2 + 30x + 65$ in vertex form. 2. **Recall the vertex form:** The vertex form of a quadratic function is

1. **State the problem:** We need to find the proper ordering of the polynomial $$14x^3 - 6x^7 + 20x^5 + 5x^2$$. 2. **Recall the rule for ordering polynomials:** Polynomials are ty

1. **State the problem:** Multiply and simplify the expression $$(3x-5)(x+2)(x+1)$$. 2. **Use the distributive property:** First multiply the last two binomials:

1. **State the problem:** We need to divide the polynomial $$6x^3 + 8x^2 - 10x$$ by $$2x$$. 2. **Write the division as a fraction:**

1. **State the problem:** We need to divide the polynomial expression $$6x^3+8x^2-10x$$ by $$2x$$. 2. **Write the division as a fraction:**

1. **State the problem:** Simplify the expression $$(2 - i) - (5 - 3i)$$ to write it as a single complex number. 2. **Recall the rule:** When subtracting complex numbers, subtract

1. **State the problem:** We need to find which of the given options is equivalent to $i^{50}$, where $i$ is the imaginary unit with the property $i^2 = -1$. 2. **Recall the powers

1. **State the problem:** We need to find the product of $5x^3$ and the expression $xy^4 - 2x^3y$. 2. **Write the expression:**

1. **State the problem:** We are given the quadratic function $$y = -x^2 + 6x - 5$$ and need to determine the vertex and the direction the parabola opens. 2. **Recall the vertex fo

1. **State the problem:** We need to multiply the complex numbers $3 - 2i$ and $4 + 2i$ and write the result as a single complex number. 2. **Recall the formula:** To multiply two

1. **State the problem:** We need to expand the expression $$(x + 8)(x - 8)$$. 2. **Recall the formula:** This is a product of conjugates, which follows the difference of squares f

1. **State the problem:** We need to subtract the polynomial $(14 - 6x)$ from $(9x^4 + 3x)$ and simplify the result. 2. **Write the expression:**

1. **State the problem:** We need to find which quadratic equation produces a parabola with vertex $(-1, 5)$. 2. **Recall the vertex form of a quadratic equation:**

1. **State the problem:** We want to solve the quadratic equation $$x^2 + 8x = -5$$ by completing the square. 2. **Recall the formula for completing the square:** For an equation o

1. **State the problem:** Match each quadratic expression to its factored form. 2. **Recall factoring formulas:**

1. **State the problem:** Simplify the expression $$(-2x)^2 x^4$$. 2. **Recall the rules:** When raising a product to a power, raise each factor to that power: $$ (ab)^n = a^n b^n

1. **State the problem:** Solve the linear equation $$3x + 4y = -8$$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables. W

1. **State the problem:** We are given that a fly equals $22$. We need to find the value of a fly with a ladybug subscript. 2. **Understand the notation:** A subscript usually deno