Division of Polynomial and Remainder Test

Is the following equation true or false? \[25x^2 \div 5x = 5x\]

Complete the equation: \(27a^2 \div \) ___ = 3a

Divide \(\frac{2x^3+4x}{2x}\)

Is the following equation true or false? \[\frac{2x+4}{x+1} = 2\]

Divide \((x^2 – 2x -3)\) by \((x + 1)\)

Is the following equation true or false? \[\frac{2x^3-5x^2-9x-3}{2x+1} = x^2-3x-3\]

Use the remainder theorem to find the remainder when \(x^3-2x^2-3\) is divided by \(x+1\).

Use the remainder theorem to find the remainder when \(x^3+3x^2-10\) is divided by \(x-1\).

For what value of \(a\) will the polynomial \(p(x)=x^3+x+a\) have remainder 2 when it is divided by \(x+2\) ?

For what value of \(b\) will the polynomial \(p(x)=x^2-bx+3\) have the same remainder when it is divided by \((x-2)\) and by \((x+1)\) ?