Question 1

Which of the following is the correct factorization by grouping of $$x^2 + 9x - 4x - 12$?

Accepted Answer

$$(x - 4)(x + 3)$$

Question 2

Given the quadratic equation $$x^2 + 5x + 6 = 0$, which of the following represents its solutions?

Accepted Answer

$$x = -2$$ and $$x = -3$$

Question 3

A chemical reaction rate is modeled by the function $$R(t) = 2t^2$ - 8t + 6. At $$what time $$t$$ does the reaction rate reach its minimum?

Accepted Answer

$$t = 2$$

Question 4

Which of the following expressions is equivalent to $$(x^2 - 16$$)$$?

Accepted Answer

$$(x - 4)(x + 4)$$

Question 5

A population of bacteria grows according to $$P(t) = 100e$$^{0.05t}$$. What is the population after 20 hours?

Accepted Answer

$$P(20) = 100e$$^{1}$$ \approx 271.83$$

Question 6

Which of the following is the correct solution set for $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6$$ and $$x = -1$$

Question 7

A projectile is launched from the ground and its height is given by $$h(t) = -16t^2$ + 64t. $$What is the maximum height reached by the projectile?

Accepted Answer

$$h_{max} = 128$$

Question 8

Which of the following is the correct factorization of $$x^2 - 5x + 6$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 9

If $$f(x) = 3x^2$ - 12x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -5)$$

Question 10

A company’s profit is modeled by $$P(x) = -2x^2$ + 20x - 32$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$P_{max} = 68$$

Question 11

Which of the following is the solution to the equation $$x^2 = 49$?

Accepted Answer

$$x = 7$$ and $$x = -7$$

Question 12

A medication’s concentration in the bloodstream is modeled by $$C(t) = 50e$$^{-0.1t}$$. What is the concentration after 10 hours?

Accepted Answer

$$C(10) = 50e$$^{-1}$$ \approx 18.39$$

Question 13

Which of the following is the correct solution to $$x^2 - 4x = 0$?

Accepted Answer

$$x = 0$$ and $$x = 4$$

Question 14

A ball is thrown upward and its height is given by $$h(t) = -9.8t^2$ + 19.6t + 2. $$How long does it take to reach its maximum height?

Accepted Answer

$$t = 1$$

Question 15

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 16

A car’s value depreciates according to $$V(t) = 20000e$$^{-0.15t}$$, where t$ is in years. What is the value after 5 years?

Accepted Answer

$$V(5) = 20000e$$^{-0.75}$$ \approx 9464.74$$

Question 17

Which of the following is the correct solution to $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Question 18

A radioactive substance decays according to $$N(t) = 500e$$^{-0.02t}$$. How much remains after 50 years?

Accepted Answer

$$N(50) = 500e$$^{-1}$$ \approx 183.94$$

Question 19

Which of the following is the correct solution to $$x^2 - 25 = 0$?

Accepted Answer

$$x = 5$$ and $$x = -5$$

Factoring Polynomials by Grouping: Precalculus Study Notes

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