Question 1

Which of the following is the correct factorization by grouping of the expression $$3x^2 - 4x - 12$?

Accepted Answer

Question 2

Given the quadratic $$3x^2 - 4x - 12$, what are its real roots?

Accepted Answer

Question 3

If you factor $$3x^2 - 4x - 12$ completely, which of the following is correct?

Accepted Answer

Question 4

Which of the following is a correct first step in factoring $$3x^2 - 4x - 12$ by grouping?

Accepted Answer

Rewrite $$-4x as$$ $$-6x + 2x$$

Question 5

After factoring $$3x^2 - 4x - 12$ by grouping, which binomial is a common factor?

Accepted Answer

$$(x - 2)$$

Question 6

A chemical reaction's rate is modeled by $$r(t) = 3t^2$ - 4t - 12. At $$what time $$t$$ does the rate become zero?

Accepted Answer

Question 7

Which of the following is the correct solution to $$3x^2 - 4x - 12 = 0$ using the quadratic formula?

Accepted Answer

Question 8

If $$3x^2 - 4x - 12$ models the height (in meters) of a projectile at time x$ seconds, when does it hit the ground?

Accepted Answer

Question 9

Which of the following is the discriminant of $$3x^2 - 4x - 12$?

Accepted Answer

$$(-4)^2 - 4$$ \cdot 3 \cdot (-12)$$

Question 10

If $$3x^2 - 4x - 12$ represents the profit (in thousands of dollars) for a company, for which x$ is the profit zero?

Accepted Answer

Question 11

Which of the following is the correct grouping to factor $$3x^2 - 4x - 12$?

Accepted Answer

$$(3x^2 - 6x) + (2x - 12$$)$$

Question 12

If you factor $$3x^2 - 4x - 12$ by grouping, what is the final factored form?

Accepted Answer

$$(x - 2)(3x + 6)$$

Question 13

Which of the following is a correct check for the factorization of $$3x^2 - 4x - 12$?

Accepted Answer

Expand $$(x - 2)(3x + 6)$$ and verify it equals $$3x^2 - 4x - 12$

Question 14

If $$3x^2 - 4x - 12$ represents the area of a rectangle in terms of x$, and the area is zero, what are the possible values of x$?

Accepted Answer

Question 15

Which of the following is the correct way to split the middle term in $$3x^2 - 4x - 12$ for factoring by grouping?

Accepted Answer

$$-4x = -6x + 2x$$

Question 16

If $$3x^2 - 4x - 12$ models the population growth of a species, for which x$ does the population reach zero?

Accepted Answer

Factoring by Grouping: Precalculus Study Notes

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