🧮 algebra

1. **State the problem:** Factor completely the expression $$28x^2 - 96x - 2x^3$$. 2. **Rewrite the expression in standard polynomial form:**

1. **State the problem:** Factor the expression $$12x - 10x^2 - 2x^3$$ completely. 2. **Identify the greatest common factor (GCF):** Each term has a factor of $$2x$$.

1. **State the problem:** Factor the expression $$8x^2 - 12x - x^3$$ completely. 2. **Rewrite the expression:** Arrange terms in descending powers of $$x$$:

1. The problem asks to find the square root of 2389 and then multiply the result by 12. 2. First, calculate the square root of 2389: $$\sqrt{2389}$$.

1. The inequality $p > 50$ means that the value of $p$ is greater than 50. 2. This is a simple inequality that sets a lower bound for $p$.

1. **سؤال 1:** ما المقطع y للدالة الأسية $4^x - 1 = y$؟ - المقطع y هو قيمة الدالة عندما $x=0$.

1. **State the problem:** We have a quartic function $$f(x) = x^4 + bx^3 + cx^2 + dx + e$$ with roots at $$x = -4, -1, 1, 3$$ and extrema at $$(-3, -50)$$ (minimum), $$(2, -20)$$ (

1. **State the problem:** Factor the expression $$15x^2 - 50x - x^3$$ completely. 2. **Rewrite the expression:** Arrange terms in descending powers of $$x$$:

1. The problem is to find the missing values A and B in the table where the function is given by $$y = 2x + 1$$ and the table has x values $$-1, 0, 1, 2, 3$$ with corresponding y v

1. The problem is to approximate the number 0.03467 to 2 significant figures. 2. Identify the first two significant figures in 0.03467. The first significant figure is 3, and the s

1. The problem asks to find 25% of 12. 2. Recall that 25% means 25 per 100, or \frac{25}{100}.

1. **Prove** $\forall x,y \in \mathbb{R}: |x - y| \leq |x| + |y|$. By the triangle inequality for real numbers, we have:

1. Problem: Prove algebraically that the sum of the squares of two odd integers is always even. Step 1: Let the two odd integers be $2m+1$ and $2n+1$, where $m$ and $n$ are integer

1. **State the problem:** We have two functions $f(x) = x^{3}$ and $g(x) = x^{2} + 1$. We want to determine which of the following functions are odd: (1) $f \times g$, meaning $(f

1. Solve the following equations by factorization. a. Solve $x^2 + 5x + 6 = 0$.

1. **State the problem:** Given that $f$ is an even function and satisfies the equation $$f(x) + x^2 f(-x) = 3,$$ find the value of $f(1)$. 2. **Recall the property of even functio

1. **State the problem:** We are given two functions $f(x) = 2x^2 + 3x - 4$ and $g(x) = x - 3$. We need to find: i) The composition $f \circ g(x) = f(g(x))$

1. **State the problem:** Solve the compound inequality $$-24 \leq -3x - 3 \quad \text{or} \quad -39 > -3x - 3$$

1. We are given the function $f(x) = \frac{3x + 2}{2x - 3}$ and asked to find the composition $(f \circ f)(x) = f(f(x))$. 2. First, substitute $f(x)$ into itself:

1. **Problem statement:** Callum leaves home at 9.00 to jog to his local shop. The distance-time graph shows parts of his trip.

1. The problem is to find the domain of the function $$f(x) = \frac{\sqrt{x-3}}{\sqrt{5-x}}.$$\n\n2. For the square root in the numerator, the expression inside must be non-negativ