Dividing polynomials Quiz 1

Question 1

Evaluate the value of $$\dfrac{{f(x)}}{{g(x)}}$$ if $$f\left( x \right) = {x^3} + 2{x^2} + x + 2$$ and $$g\left( x \right) = {x^2} + 1$$.

Accepted Answer

$$x + 2$$

Answer

$$x + 1$$

Answer

$$2x + 1$$

Answer

$$x + 3$$

Question 2

Calculate the value of $$\dfrac{{f(x)}}{{g(x)}}$$ if $$f\left( x \right) = {x^4} + 4{x^3} + 3{x^2} + 2x + 2$$ and $$g\left( x \right) = x + 1$$.

Accepted Answer

$${x^3} + 3{x^2} + 2$$

Answer

$${x^3} + 5{x^2} - 1$$

Answer

$${x^3} + {x^2} + x + 1$$

Answer

$${x^3} + 2{x^2} + 2$$

Question 3

The value of quotient and remainder if the polynomial $${x^5} + 3{x^4} + 2{x^3} + 2{x^2} - 3x$$ is divided by $${x^2} + 1$$ is

Accepted Answer

$${x^3} + 3{x^2} + x - 1;\; - 4x + 1$$

Answer

$${x^3} + 3{x^2} + 4;\;3x + 8$$

Answer

$$3{x^3} - 2{x^2} + 2;\;4x + 8$$

Answer

$${x^3} - 2{x^2} + 4;\;4x - 8$$

Question 4

Evaluate the degree of $$\dfrac{{f(x)}}{{g(x)}}$$ if $$f\left( x \right) = 3{x^3} + 6{x^2} + 3x + 6$$ and $$g\left( x \right) = {x^2} + 1$$ is

Accepted Answer

$$1$$

Answer

$$2$$

Answer

$$3$$

Answer

$$0$$

Question 5

Evaluate the degree of $$\dfrac{{f(x)}}{{g(x)}}$$ if $$f\left( x \right) = 4{x^3} - 12{x^2} + 8x - 24$$ and $$g\left( x \right) = x - 3$$ is

Accepted Answer

$$2$$

Answer

$$4$$

Answer

$$3$$

Answer

$$1$$