🧮 algebra

1. Solve each equation by factoring. ### a) $x^4 - 16x^2 + 75 = 2x^2 - 6$

1. State the problem. Determine the x-intercept(s) of the function $y=3(x+6)^4-48$.

1. **Problem statement:** We analyze the relations given by the equations $$x^{2} + y^{2} = 25$$ and $$y = \\sqrt{25 - x^{2}}$$ to graph them, determine whether they are functions,

1. The problem provides two quartic functions and their graph transformations. 2. First function: $y = \frac{5}{4}x^4 + 3$.

Problem: Factor $x^2 + 5x - 6$. 1. Identify the coefficients for the quadratic in the form $ax^2 + bx + c$: we have $a=1$, $b=5$, and $c=-6$.

1. **Stating the problem**: Given $\log_4 x = y$, where $x > 0$, find: a) $\log_2 x$

1. The problem asks for equations of lines passing through the point $(2, -5)$ under different conditions. 2. (a) A line with slope $-3$ passing through $(2,-5)$:

1. The problem is to factor the quadratic expression $$x^2 + 5x + 6$$. 2. We look for two numbers that multiply to the constant term 6 and add up to the coefficient of the linear t

1. The problem is to factor the expression $x^2$. 2. Notice that $x^2$ is a perfect square since it is $x$ multiplied by itself.