Division of polynomial and remainder theorem

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Question 1:
1 pts
Is the following equation true or false? $$25x^2 \div 5x = 5x$$
Question 2:
1 pts

$27a^2 \div $

$=3a$
Question 3:
1 pts
Divide $\frac{2x^3+4x}{2x}$

$x^2+2x$

$x+2$

$2x+2$

$x^2+2$
Question 4:
1 pts
Is the following equation true or false? $$\frac{2x+4}{x+1} = 2$$
Question 5:
2 pts
Divide $(x^2 - 2x -3)$ by $(x + 1)$

$x-3$

$x+3$

$x-2$

$x+2$
Question 6:
2 pts
Is the following equation true or false? $$\frac{2x^3-5x^2-9x-3}{2x+1} = x^2-3x-3$$
Question 7:
3 pts
Use the remainder theorem to find the remainder when $x^3-2x^2-3$ is divided by $x+1$.

$6$

$-4$

$4$

$-6$
Question 8:
3 pts
Use the remainder theorem to find the remainder when $x^3+3x^2-10$ is divided by $x-1$.

$5$

$-5$

$-6$

$-8$
Question 9:
3 pts
For what value of $a$ will the polynomial $p(x)=x^3+x+a$ have remainder 2 when it is divided by $x+2$ ?

$a = 10$

$a = 11$

$a = 12$

$a = 13$
Question 10:
3 pts
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 $(x+1)$ ?

$b = 1$

$b = 2$

$b = 3$

$b = 4$

Basics of polynomials

$x-3$	$x+3$
$x-2$	$x+2$

$6$	$-4$
$4$	$-6$

$5$	$-5$
$-6$	$-8$