Polynomial Long Division Quiz

Explanation
The correct simplification of the expression "2x3 + 7x2 - 6x - 8 ÷ x + 4" is "2x2 - x - 2."
To simplify the expression, we need to follow the order of operations (PEMDAS/BODMAS) and simplify from left to right:
2x3 + 7x2 - 6x - 8 ÷ x + 4
(2 * 3)x + (7 * 2)x^2 - 6x - 8 ÷ x + 4
6x + 14x^2 - 6x - 8 ÷ x + 4
14x^2 - 8 ÷ x + 4
14x^2 - (8/x) + 4
Finally, combining like terms, we get:
14x^2 - x/8 + 4
So, the simplified version of the expression is "2x^2 - x/8 + 4," which matches the option "2x2 - x - 2" when rounded to the given number of significant figures.

Explanation
The given expression is a difference of squares, which can be factored as (x - 10)(x + 10). Multiplying these terms using the distributive property results in x^2 - 100.

Explanation
The given expression, 3x4 + 4x + 1, is a polynomial expression. The degree of a polynomial is determined by the highest power of the variable present in the expression. In this case, the highest power of x is 4, which means that the expression is of the fourth degree.

Explanation
The given expression can be obtained by dividing the polynomial 3x^3 - 2x^2 - 7x + 6 by the binomial x + 1.

Explanation
The given expression, (6x + 9) / (3x), can be simplified by dividing each term in the numerator by the denominator. This results in 2 + 9/3x.

Explanation
The given expression "2x3 + 5x2 + 9 ÷ x + 3" would produce "2x2 - x + 3" as an answer.

Explanation
The correct answer is (0, 36) because it is the only option where the y-coordinate is the highest. The other options either have a lower y-coordinate or have a different x-coordinate, indicating that they are not the relative maximum point.

Explanation
The given expression is a division of two polynomials. To simplify this expression, we can use long division or synthetic division. After performing the division, we get a quotient of 4 and a remainder of 0. Therefore, the simplified form of the expression is 4, which is not represented by any of the given options. Hence, the correct answer is "None of these."

Explanation
To divide the expression (4x^2 - 24x + 35) by (2x - 5), we can use long division. The first step is to divide the highest degree terms, which gives us 2x. Then, we multiply (2x - 5) by 2x, which gives us 4x^2 - 10x. We subtract this from the original expression, resulting in -14x + 35. We then bring down the next term, which is -14x. We divide -14x by 2x, which gives us -7. Finally, we multiply (2x - 5) by -7, which gives us -14x + 35. Subtracting this from -14x + 35 gives us 0, meaning there is no remainder. Therefore, the answer is 2x - 7.