Question 1

Which of the following is the correct first step when solving the polynomial equation $$x^3$$ - $$4x^2 + x = 6$?

Accepted Answer

Set the equation equal to zero by subtracting 6 from both sides: $$x^3$$ - $$4x^2 + x - 6 = 0$.

Question 2

Given the equation $$x^3$$ - $$2x^2 - 8x = 0$, which of the following is the correct factorization?

Accepted Answer

$$x(x - 4)(x + 2) = 0$$

Question 3

How many possible real solutions does the polynomial equation $$x^4$$ - $$5x^2 + 6 = 0$ have?

Accepted Answer

4

Question 4

A chemical reaction is modeled by the equation $$t^3$$ - $$7t^2 + 10t = 0$, where t$ is time in seconds. What are the possible times when the reaction is at equilibrium?

Accepted Answer

$$t = 0, 2, 5$$

Question 5

Which of the following is NOT a valid step in solving the equation $$x^3$$ + $$2x^2 - 8x = 0$?

Accepted Answer

Dividing both sides by $$x$$ before factoring.

Question 6

Solve the equation $$x^3 - 9x = 0$ and select the correct set of solutions.

Accepted Answer

$$x = 0, 3, -3$$

Question 7

A population model is given by $$P^3$$ - $$6P^2 + 9P = 0$. What are the possible population sizes at equilibrium?

Accepted Answer

Question 8

Which of the following equations is a polynomial equation of degree 4?

Accepted Answer

$$x^4$$ - $$2x^2 + 1 = 0$

Question 9

If $$x^3$$ - $$6x^2 + 11x - 6 = 0$, which of the following is a correct factorization?

Accepted Answer

$$(x - 1)(x - 2)(x - 3) = 0$$

Question 10

A medical dosage model is given by $$d^2(d - 4) = 0$. What are the possible dosages d$ that result in zero effect?

Accepted Answer

$$d = 0, 4$$

Question 11

Which of the following statements about solving polynomial equations is TRUE?

Accepted Answer

The degree of the polynomial tells you the maximum number of solutions.

Question 12

Solve the equation $$x^4$$ - $$5x^2 + 4 = 0$ and select the correct set of real solutions.

Accepted Answer

Question 13

A business profit model is given by $$p^3$$ - $$4p^2 = 0$. What are the possible profit values p$ at equilibrium?

Accepted Answer

Question 14

Which of the following is the correct way to check your solutions after solving a polynomial equation?

Accepted Answer

Substitute each solution back into the original equation to verify it equals zero.

Question 15

If a polynomial equation has degree 5, what is the maximum number of real solutions it can have?

Accepted Answer

5

Question 16

Which of the following is a necessary step when solving $$x^3$$ + $$2x^2 - 8x = 0$?

Accepted Answer

All of the above.

Question 17

A historical population decline is modeled by $$n^3 - 9n = 0$. What are the possible population sizes n$ at which the population stabilizes?

Accepted Answer

$$n = 0, 3, -3$$

Question 18

Which of the following is a polynomial equation with degree greater than 2?

Accepted Answer

$$x^3 - 2x + 1 = 0$

Solving Polynomial Equations: Methods and Examples

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