Solve the qudaratic equation by factorization x^2+x-(a+1)(a+2)=0

Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If it is​ not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.
$g(x)=3-\frac{x^2}{4}$

To prove ${\displaystyle a{x}^2+bx+c\equiv a{y}^2+by+c\left(b\mathrm{mod}m\right)}$ if a, b and c are integers and ${\displaystyle x\equiv y\left(b\mathrm{mod}m\right)}$.

Factor completely each polynomial, and indicate any that are not factorable using integers. ${\displaystyle a^{2}x+b^{2}x+a^{2}y+b^{2}y}$

Factor completely each polynomial, and indicate any that are not factorable using integers. ${\displaystyle x^2-7x-8}$

The value of the operation ${\displaystyle {\left[11\right]}^9}$ in ${\displaystyle Z_{12}}$ and to write the answer in the form [r] with ${\displaystyle 0\le r<m}$.

Find all the real zeros of teh polynomial. Use the Quadratic Formula if necessary given.
${\displaystyle P\left(x\right)=4x^3-6x^2+1}$

Solve system of equation by chinese remainder theorem:
${\displaystyle x\equiv 5\left(b\text{mod}24\right)}$
${\displaystyle x\equiv 17\left(b\text{mod}18\right)}$