Factoring monomials Quiz 1

Question 1

Simplify the factorial  $$\dfrac{{(2k - 1)!}}{{(2k + 2)!}}$$

Accepted Answer

$$\dfrac{1}{{(2k + 2)(2k + 1)(2k)}}$$

Answer

$$\dfrac{1}{{(2k + 3)(2k + 1)(2k)}}$$

Answer

$$\dfrac{1}{{(2k + 2)(k + 1)(2k)}}$$

Answer

$$\dfrac{1}{{(2k + 2)(2k + 1)(2k - 1)}}$$

Question 2

Calculate the roots of the given expression $$\dfrac{{(5k + 2)!}}{{(5k - 1)!}} = 0$$

Accepted Answer

$$k = 0,k =  - \dfrac{1}{5},k =  - \dfrac{2}{5} $$

Answer

$$k = 0,k =  - \dfrac{1}{5},k =  - 1 $$

Answer

$$k =  - 1,k =  - \dfrac{1}{5},k =  - \dfrac{2}{5} $$

Answer

$$k = 0,k =  - \dfrac{5}{2},k =  - \dfrac{2}{5} $$

Question 3

How many roots satisfies the equation $${k^2} + 3k + 2 = 0$$, if the expression is following $$ \ \dfrac{{{{((k + 2)!)}^3}}}{{{{((k - 1)!)}^2}}} = 0$$

Accepted Answer

Two roots, $$k =  - 2, k =  - 1$$

Answer

Two roots, $$k = 0, k =  - 1$$

Answer

Two roots, $$k = 0, k =  - 2$$

Answer

Three roots, $$k = 0, k =  - 1, K =  - 2$$

Question 4

Simplify the given expression $$\dfrac{{({k^2} - 9)!}}{{(k - 3)({k^2} - 10)!)}}$$

Accepted Answer

$$(k + 3)$$

Answer

$$(k + 10)$$

Answer

$$(k - 3)$$

Answer

$$(k + 9)$$

Question 5

Calculate the value of the equation $${k^2} + 5k + 6$$, if the expression is following $$ \ \dfrac{{{{((k + 3)!)}^{35}}}}{{{{((k - 1)!)}^{35}}{{(k + 3)}^{35}}{{(k + 2)}^{35}}{{(k + 1)}^{35}}{k^{35}}}} = 0$$

Accepted Answer

$$1056$$

Answer

$$ - 1065$$

Answer

$$1065$$

Answer

$$ - 1056$$