Question 1

Which pair of numbers can be used to factor $$x^2 + 18x + 81$?

Accepted Answer

$$9$$ and $$9$$

Question 2

What is the factored form of $$x^2 - 13x + 40$?

Accepted Answer

$$(x - 5)(x - 8)$$

Question 3

Given $$x^2 + 3x - 54$, which two numbers multiply to -54$ and add up to 3$?

Accepted Answer

$$9$$ and $$-6$$

Question 4

What is the greatest common factor (GCF) of $$5x^2 + 75x + 270$?

Accepted Answer

$$5$$

Question 5

Factor completely: $$-4x^2 - 44x + 104$.

Accepted Answer

$$-4(x^2 + 11x - 26$$)$$

Question 6

Which is the correct factorization of $$x^2 - 2x - 35$?

Accepted Answer

$$(x - 7)(x + 5)$$

Question 7

A chemical reaction produces a quadratic equation for concentration: $$c^2 + 6c + 8 = 0$. What are the possible concentrations?

Accepted Answer

$$-2$$ and $$-4$$

Question 8

What is the GCF of $$5x^3$$ + $$55x^2 + 120x$?

Accepted Answer

$$5x$$

Question 9

A projectile's height is modeled by $$h(t) = t^2$ - 11t + 30. At $$what times does the projectile hit the ground?

Accepted Answer

$$t = 5$$ and $$t = 6$$

Question 10

Which is the correct factorization of $$m^2 + 9m + 18$?

Accepted Answer

$$(m + 6)(m + 3)$$

Question 11

A business's profit is modeled by $$P(x) = x^2$ + 4x - 12. $$For which values of $$x$$ does the profit become zero?

Accepted Answer

$$x = -6$$ and $$x = 2$$

Question 12

What is the factored form of $$a^2 + 4a + 3$?

Accepted Answer

$$(a + 3)(a + 1)$$

Question 13

Which is the correct factorization of $$x^2 - 7x + 12$?

Accepted Answer

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

Question 14

A quadratic equation $$x^2 + 13x + 24$ models the number of bacteria in a culture. What are the possible values for x$?

Accepted Answer

$$-12$$ and $$-1$$

Question 15

What is the GCF of $$2x^2 + 24x + 22$?

Accepted Answer

$$2$$

Question 16

Which pair of numbers can be used to factor $$x^2 + 6x + 8$?

Accepted Answer

$$2$$ and $$4$$

Question 17

A quadratic equation $$x^2 + 4x - 12$ models the height of a ball. What are the roots?

Accepted Answer

$$x = -6$$ and $$x = 2$$

Question 18

Which is the correct factorization of $$x^2 + 14x + 49$?

Accepted Answer

$$(x + 7)^2$

Question 19

A quadratic equation $$x^2 - 3x - 54$ models the number of patients in a hospital. What are the possible values for x$?

Accepted Answer

$$x = 9$$ and $$x = -6$$

Factoring Quadratic Expressions and Greatest Common Factor (GCF): Precalculus Study Notes

Guida di studio - Domande di pratica