Expert Answers to Algebra 2 Problems

Solve the following quadratic equations by factorization method:
${\displaystyle \frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15},x\ne 0,x\ne -1}$.

Solve the following quadratic equation by factorization.
${\displaystyle \frac{2x}{x-3}+\frac{1}{2x+3}+\frac{3x+9}{(x-3)(2x+3)}=0}$

In how many ways can 8 people be seated in a row if a.) there are no restrictions on the seating arrangement(answer is ${\displaystyle 8!=40,320}$) , b.) persons A and B must sit next to each other? (Answer: 10,080) , c.) there are 4 men and 4 women and no 2 men or 2 women can sit next to each other? (Answer: 1,152) , d.) there are 5 men and they must sit next to one another? (Answer: 2,880) , e.) there are 4 married couples and each couple must sit together? (Answer: 384). I need to see the steps to solve questions 10b to 10e. I quickly looked through the corresponding chapter on combinatorial analysis and I went over topics such as the multinomial theorem, the basic principle of counting, the binomial theorem, and representing the number of possible combinations of n objects taken r at a time as "n choose r" .

Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
(x-4)(x+2)

Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
(-2x-3y)(3x+2y)

Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
(x-2y)(x+y)

Multiply each function out and find the derivative of the higher-order polynomial.
(4x+6)(9x-5)

Factor the polynomial. ${\displaystyle 81r^2-16t^2}$.

Find the Taylor polynomial ${\displaystyle T3\left(x\right)}$ for the function f centered at the number a.
${\displaystyle f\left(x\right)=x+e^{-x},a=0}$
${\displaystyle T3\left(x\right)=}$?

How to graph ${\displaystyle y=3^{-x}}$

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.
${\displaystyle {(x-1)}^2-2(x-1)}$

How do you solve ${\displaystyle \log \left(x\right)=-0.123}$

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form.
${\displaystyle P\left(x\right)=x^4-5x^2+4}$

Add the polynomial
${\displaystyle -2(4x^7+3x^9+2x^8)+(-9x^9-8x^7+3+5x^9)}$

Taylor polynomials Find the nth-order Taylor polynomial for the following functions centered at the given point a.
${\displaystyle f\left(x\right)=\sin 2x,n=3,a=0}$

Multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form.
(3x+y)(3x-4y)

Multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form.
(3x+2)(3x-2)

Multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form.
${\displaystyle {(3x-4)}^2}$

Factor completely each polynomial, and indicate any that are not factorable using integers. ${\displaystyle 18n^3+39n^2-15n}$

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.
x(x+3)-6(x+3)