Expert Answers to Algebra 2 Problems

What is a polynomial function?

Construct the augmented matrix that corresponds to the following system of equations.
${\displaystyle 5+\frac{8x}{5}=y}$
4z−3(x−4y)=0
5x−y=3(x−6z)

To simplify:
The given expression ${\displaystyle \sqrt{x^3}}$

To simplify:
The given expression ${\displaystyle \sqrt{s\sqrt{s^3}}}$

How to solve ${\displaystyle x^2-6x+9=20}$ using the Square Root Property

Prove the Arithmetic-Geometric Mean Inequality If ${\displaystyle a_1{a}_2,\dots ,a_n}$ are nonnegative numbers, then their arithmetic mean is ${\displaystyle \frac{a_1+a_2+\dots +a_n}{n},}$ and their geometric . The avthmetic-geometic mean is ${\displaystyle \sqrt{n}\{a_1,a_2,\dots a_n\}.}$ The arithmetic-geometric mean equality states that the geometric mean is always less than or equal to the arithmetic mean. In this problem we prove this in the case of two numbers andy. (a) If x and y are nonnegative and ${\displaystyle x\le y,then{x}^2\le y^2.}$ [Hint: First use Rule 3 of Inequalities to show that ${\displaystyle x^2\le xy\text{and}xy\le y^2.}$ ] (b) Prove the arithmetic-geometric mean inequality ${\displaystyle \sqrt{xy}\le \frac{x+y}{2}}$

${\displaystyle \log 3\left(\frac{1}{9}\right)}$

prove that for all rational numbers r and s, rs is rational

${\displaystyle \log 5\cdot 5^4}$

Write P into factored form
${\displaystyle P\left(x\right)=x^3+3x^2+4x+12}$

Whether the statement “When performing the division $\frac{x^5+1}{x+1}$ there's no need for me to follow all the steps involved in polynomial long division because I can work the problem in my head and see that the quotient must be $x^4+1$ ”makes sense or not.” Makes sense or not.

Find the exponential function that models the data in the table below. $\overline{)\begin{array}{ccccccccc}x& -3& -2& -1& 0& 1& 2& 3& 4\\ y& 4/27& 4/9& 4/3& 4& 12& 36& 108& 324\end{array}}$ What is the exponential regression of the data? $y=square$ 

Whether tha addition, subtraction, pultiplication and division of polynomials always result in a polynomial or not. Explain reason.

Find the binomial that completes the factorization.
${\displaystyle 5s^4+5000s{t}^3=5s(s^3+1000t^3)}$

Factor the polynomial completely.
xy+11x-5y-55

If $\log 3=A\text{ and }\log 7=B$, find
${\log }_{7}9$
in terms of A and B.

To calculate: The simplified form of the expression, $\frac{8-\sqrt{48}}{6}$

1. Explain with numerical examples what Real Numbers and Algebraic Expressions are. 2. Explain with numerical examples Factoring and finding LCMs (least common multiples). Explain factoring of a larger number. 3. Explain with numerical examples arithmetical operations (addition, subtraction, multiplication, division) with fractions 4, Explain with numerical examples arithmetical operations (addition, subtraction, multiplication, division) with percentages 5. Explain with numerical examples exponential notation 6. Explain with numerical examples order (precedence) of arithmetic operations 7. Explain with numerical examples the concept and how to find perimeter, area, volume, and circumference (use related formulas)

Need to calculate:The factorization of $2x^3-8x^2-9x+36$.