🧮 algebra

1. **State the problem:** We need to fully factorise the quadratic expression $$3t^2 + 16t + 5$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look fo

1. **State the problem:** We need to fully factorise the quadratic expression $$5q^2 - 17q - 12$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$

1. **State the problem:** Fully factorise the quadratic expression $$2x^2 - 13x + 15$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numb

1. **State the problem:** We are given two equations: $$\frac{5a - 3}{9} = 3$$

1. **State the problem:** Solve the inequality $$\frac{-2z-3}{3} < 5$$. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator

1. **State the problem:** Helen rents a kayak with an initial fee plus an hourly charge. The total cost is $20$. We need to find the number of hours she kayaked. 2. **Define variab

1. **Problem Statement:** Complete the square for each quadratic expression of the form $$ax^2 + bx + c$$ by factoring out the common factor from the first two terms, completing th

1. **State the problem:** We need to graph the quadratic function $$y = -x^2 + 6x - 8$$ and plot 5 points including the roots and the vertex. 2. **Formula and important rules:** Th

1. Sprawdźmy pierwszą równość: $$\sqrt{1,96} + \sqrt[3]{0,125} = ? 1,8$$

1. **Stwierdzenie problemu:** Obliczymy wartości wyrażeń:

1. **State the problem:** We need to subtract $-3 - (-6)$. This means subtracting a negative number from another negative number. 2. **Rewrite subtraction as addition:** Recall the

1. **State the problem:** We need to subtract $6$ from $-2$, which is written as $-2 - 6$. 2. **Rewrite subtraction as addition:** Subtraction of a number is the same as adding its

1. **State the problem:** We want to subtract $9 - 12$ and rewrite it as an addition of signed numbers. 2. **Rewrite subtraction as addition:** Subtraction of a number is the same

1. **State the problem:** We want to subtract $12$ from $3$, i.e., compute $3 - 12$. 2. **Rewrite subtraction as addition:** Subtraction can be rewritten as addition of the opposit

1. **State the problem:** We need to add the two rational numbers $-3$ and $-2$. 2. **Recall the rule for adding negative numbers:** When adding two negative numbers, you add their

1. **State the problem:** We need to divide the polynomial $32a^3 + 8a^2 - 7a - 16$ by $-8a$ and simplify the result. 2. **Write the division as separate terms:**

1. **State the problem:** We need to divide the polynomial $$6c^{10} - 18c^8 + 14c^4$$ by $$2c^4$$ and simplify the result. 2. **Write the division as separate terms:**

1. **State the problem:** We need to find the speeds of Cameron's and Ellia's electric scooters given that Cameron's speed is 6 mph faster than Ellia's and they travel different di

1. **State the problem:** We need to find the speeds of bus A and bus B given that bus A is 14 mph slower than bus B and both travel different distances in the same time.

1. **State the problem:** We need to find the speeds of two trains: a passenger train and a freight train. The freight train's speed is 8 mph less than the passenger train's speed.

1. **State the problem:** We need to find the time it takes to fill the pool when both the pipe and the hose are working together. 2. **Identify rates:** The pipe fills the pool in