We need to determine if x-5 is a factor of 2x^{3} - 4x^{2} - 7x - 10

A ball is tossed upward from the ground. Its height in feet above ground after t seconds is given by the function ${\displaystyle h\left(t\right)=-16t^2+24t}$. Find the maximum height of the ball and the number of seconds it took for the ball to reach the maximum height.

How do you write 3.141 in expanded notation?

Evaluate fraction of sum
So i have to evaluate this sum:
${\displaystyle \frac{1-2^{-2}+4^{-2}-5^{-2}+7^{-2}-8^{-2}+{10}^{-2}-{11}^{-2}+\cdots }{1+2^{-2}-4^{-2}-5^{-2}+7^{-2}+8^{-2}-{10}^{-2}-{11}^{-2}+\cdots }}$
it has the form : ${\displaystyle \frac{\sum _0^{\mathrm{\infty }}[{(3n+1)}^{-2}-{(3n+2)}^{-2}]}{\sum _0^{\mathrm{\infty }}{(-1)}^n[{(3n+1)}^{-2}+{(3n+2)}^{-2}]}}$
My current attempt : Trying to convert this into power series
${\displaystyle a\left(n\right)={(3n+1)}^{-2}-{(3n+2)}^{-2}b\left(n\right)={(3n+1)}^{-2}+{(3n+2)}^{-2}}$
Can a(n) and b(n) be the definite integral of certain polynomial function f(x) ?
Maybe there is a better direction. Can someone give me a hint ?

The mean distance of Earth from the Sun is ${\displaystyle 9.29\times 1079.29\times {10}^7}$ miles. The orbit of Earth around the Sun is circular and that 1 revolution takes 365 days; find the linear speed of Earth.

Let ${\displaystyle f\left(x\right)=3-(x+4)+2x}$ . How do you find all values of x for which f(x) is at least 6?

How do you solve ${\displaystyle p+9>-3}$ ?