Practice Test 72 - Algebra 2

20 questions. Answer them in any order, then submit to see your score and every explanation.

Recognize $x^4-16$ as a difference of squares (possibly more than once) and factor it completely over the integers using polynomial identities.
Use technology (calculator or software) to solve the system by the inverse-matrix method. Write it in matrix form $AX=B$ , then compute $X=A^{-1}B$ . $\begin{cases} x+2y-z=4\\ 2x-y+z=1\\ x+y+2z=8 \end{cases}$ What is $X=\begin{bmatrix}x\\y\\z\end{bmatrix}$ ?
A savings plan adds $40 each month. The balances at the end of each month are: Month: 0, 1, 2, 3 Balance ($): 200, 240, 280, 320 Is the growth rate constant additive (linear) or constant percent (exponential)?
Solve using the quadratic formula and simplify: $2x^2-3x-7=0.$
For $p(x)=x(x-2)^2(x+1),$ which statement correctly gives the zeros (and crossing/touching behavior) and the end behavior?
The function $f(x)=-x^2+10$ is not invertible on all real numbers because it fails the horizontal line test. Which domain restriction makes $f$ one-to-one?
The expression $2x^2 - 8x - 42$ can be factored to reveal its zeros. Which of the following correctly identifies all zeros of the function $f(x) = 2x^2 - 8x - 42$ ?
Describe the end behavior of the polynomial function $f(x)=-3x^5+2x^3-7.$
Over the complex numbers, every quadratic equation $ax^2+bx+c=0$ has exactly 2 solutions counting multiplicity. The discriminant $b^2-4ac$ determines the type: $>0$ gives two distinct real solutions, $=0$ gives one repeated real solution (multiplicity 2), and $<0$ gives two complex conjugates. For $x^2+2x+5=0$ , which option correctly gives the discriminant sign and all complex solutions?
Solve the quadratic equation $x^2+2x+10=0$ and express the solutions as complex numbers in the form $a\pm bi$ .
Use polynomial division to rewrite $\dfrac{2x^4+x^3-3x^2+5}{x^2-1}$ in the form $q(x)+\dfrac{r(x)}{x^2-1}$ , where $\deg(r)<2$ .
What is the horizontal asymptote of $f(x)=\frac{3x^2-x+7}{2x^2+5}?$
If $\log_5(a) + 3\log_5(b) - \log_5(c) = \log_5(20)$ , which equation is equivalent using logarithm properties?
If $z = -2 + 5i$ , what is $|z|^2$ calculated using the conjugate method?
A chemical reaction rate is modeled by $R(T) = k \cdot 3^{(T-298)/10}$ , where $T$ is temperature in Kelvin and $k$ is a constant. To convert this to Celsius ( $C = T - 273$ ), which form correctly expresses the rate in terms of Celsius temperature?
Use the product, quotient, and power properties of logarithms to write the following as a single logarithm (base 10): $2\log(x) + \frac{1}{2}\log(y) - 3\log(z).$
If the remainder when $p(x)=x^3-2x^2+kx-5$ is divided by $(x-1)$ is $3$ , find $k$ . (Use $ \text{remainder} = p(1) $.)
Sound level in decibels is modeled by $\text{dB}=10\log_{10}\left(\dfrac{I}{I_0}\right)$ , where $I$ is the sound intensity and $I_0$ is a reference intensity. If a sound has intensity $500$ times the reference (so $I/I_0=500$ ), create an equation and find its sound level in decibels. Round to the nearest tenth and interpret your result in context.
A student claims that for any complex number $z = a + bi$ , the expression $z + \overline{z}$ always equals $2a$ . To verify this claim using $z = -3 + 7i$ , what calculation should be performed?
A savings plan deposits money at the end of each month. The first deposit is $100, and each month the deposit is multiplied by $1.05$ (a 5% increase). What is the total amount deposited after $6$ months (ignore interest on the account itself)?

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