log_2(8) = 3 and log_2(4) = 2, thus log_2(8) + log_2(4) = 3 + 2 = 5.

Substituting x = 1 into P(x) gives P(1) = 1^3 - 3(1^2) + 4 = 2.

Substituting x = -1 gives P(-1) = 5(-1)^2 - 3(-1) + 7 = 5 + 3 + 7 = 15.

To solve for x, add 9 to both sides and then divide by 3: 3x = 9, thus x = 3.

The author acknowledges the importance of education but also points out that it is not the only solution to inequalities.

Since the leading coefficient is negative and the degree is even, both ends of the graph will go to negative infinity.

The passage indicates that access to quality education is a significant factor in reducing inequality.

The passage suggests that education plays a crucial role in mitigating social inequalities, highlighting its importance.

Dependent systems have infinitely many solutions as they represent the same line.

A polynomial that includes a variable in the denominator is not a polynomial function.

Since the leading coefficient is negative and the degree is even, both ends of the polynomial go down.

Distributing 2 gives 2 * x + 2 * 3 = 2x + 6.

Using the property of exponents that states a^m * a^n = a^(m+n), we combine the exponents: 2x + (x + 1) = 3x + 1.

Since 1000 is 10^3, log_10(1000) = 3.

The vertex of the quadratic equation is given by the point (-b/2a, f(-b/2a)).

The function f(x) = 1/(x - 2) has a vertical asymptote at x = 2, where the function is undefined.

A horizontal line represents a function that is constant, meaning it neither increases nor decreases.

A quadratic function is represented by a parabola, which can open either upwards or downwards.

Exponential functions grow or decay at a constant percentage rate, which is a defining characteristic.

The y-intercept is defined as the point where the line crosses the y-axis, which occurs when x is zero.

The polynomial x^2 - 9 can be factored as (x - 3)(x + 3).

The roots of the polynomial can be found by factoring it as (x-2)(x-3) = 0, giving roots 2 and 3.

All listed methods are valid for solving systems of linear equations.

In a geometric progression, the common ratio cannot be zero, as it would invalidate the progression.

The sum of the terms in a harmonic progression is not necessarily an integer, as the terms can be fractions.

The sum of the first n terms of a harmonic progression diverges as n approaches infinity, hence it is not finite.

The last statement is incorrect as it does not follow the properties of logarithms.

The quadratic x^2 - 5x + 6 factors to (x - 2)(x - 3).

All the listed properties are correct and fundamental to logarithmic functions.

Using the power of a product property, (a*b)^n = a^n * b^n, we get (x^3)^2 * (y^2)^2 = x^6 * y^4.