December 2020

Solve for y if $y = e^{\ln \sqrt{x}}$.

Solve for y if $y = (e^x + e^{-x})^2 - (e^x - e^{-x})^2$.

Solve for x if $\dfrac{e^x + e^{-x}}{2} = 1$.

Solve for x if $x = \log \left[ 10 \log (5 \log 100) \right]^3$.

Solve for x from the given equation: 2^x · 2^{x + 1} = 128.

When x² + 5x - 2 is divided by x + n, the remainder is -8. Find all possible values of n.

Solve for x if

$$\dfrac{3(2x - 1)^{1/2}}{x - 3} - \dfrac{(2x - 1)^{3/2}}{(x - 3)^2} = 0$$

Is $x - 2$ a factor of $x^3 - 3x^2 + 7x - 10$?

Using synthetic division, find the quotient if $2x^3 - 9x^2 + 10x - 3$ is divided by $x - 3$.

Find the quotient of $x^3 - x^2 - 5x + 6$ divided by $x - 2$.