🧮 algebra

1. We start with the polynomial equation $x^4 - 2x^3 - 7x^2 + 8x + 12 = 0$. 2. Factor using rational root theorem or synthetic division to find roots.

1. Problem 48: Given a triangle with base $3x + 4$ cm and height $2x - 1$ cm, area $17.5$ cm², form an equation for $x$ and show it reduces to $6x^2 + 5x - 39 = 0$. Then find the p

1) Développe et réduis 1. Développons $(\sqrt{7} - 7)^2$ :

1. The problem is to simplify the expression $4x + x$. 2. Identify the like terms in the expression: both terms have the variable $x$.

1. **State the problem:** We are given the quadratic equation $$3x^2 - 6x - 4 = 0$$ with roots $$\alpha$$ and $$\beta$$. 2. **Find the sum and product of the roots:** For a quadrat

1. Stating the problem: We have the cubic function $$F(x) = -x^3 + 2x^2 - 9x - 15$$. 2. From the table and given values, it seems we want to analyze the roots or evaluate the funct

1. Let's analyze the system of inequalities for each case and find the feasible regions. 2. For A:

1. Stating the problem: Solve the equation $$|X + 1| = 5$$. 2. Recall that absolute value equation $$|A| = B$$ (where $$B \geq 0$$) can be rewritten as two separate equations: $$A

1. **State the problem**: Given the cubic function $$F(x) = -\frac{1}{9}x^3 + 7x^2 - 7x - 15,$$ find its roots, critical points, and analyze sign changes. 2. **Find roots of the fu

1. Stating the problems: We are solving for $x$ in the absolute value equations:

1. The problem states we have two parabolic curves derived from birth months and years. 2. For the father: birth month is June (6), birth year ends with 20.

1. Simplify expression 3a + 6b by factoring out the common factor 3: $$3a + 6b = 3(a + 2b)$$

1. Sketch the graph of each function. **1) $y = 2x^2 + 6x$**

1. **State the problem:** Expand the expression $ (5x + 2y)(3x - 2y) $. 2. **Apply the distributive property (FOIL method):** Multiply each term in the first parenthesis by each te

1. **State the problem:** Solve the quadratic equation $$x^2 - 6x + 9 = 1$$ using square roots and check the solutions. 2. **Rewrite the equation:** Subtract 1 from both sides to s

1. **State the problem:** We want to find a whole number $x$ such that the sum of $x$ and twice the square of $x$ equals 10. 2. **Write an equation:** The problem translates to the

1. **Write the equation of a line parallel to** $3x - 2y + 5 = 0$ **and passing through** $(1,1)$. - Lines parallel have the same slope. First, rewrite the given line in slope-inte

1. The problem gives us two points: Laurie at $(-5,30)$ and Anne at $(23,9)$, and mentions a fountain halfway between them. 2. To find the fountain's coordinates, we calculate the

1. **State the problem:** Simplify the expression $$\sqrt{7 - t} + \sqrt{7 + t}$$ and determine when its value is a natural number (i.e., an integer greater than or equal to 1). 2.

1. Problem 7: If four times a whole number is subtracted from three times the square of the number, the result 15 is obtained. Find the number. Step 1: Let the whole number be $x$.

1. Stated problem: Factor the quadratic expression $x^2 + 5x + 6$. 2. To factor, find two numbers that multiply to $6$ (the constant term) and add to $5$ (the coefficient of $x$).