Quiz about Mastering Quadratic Functions Through Factoring

Question 1

Solve the quadratic equation by factoring: $$x^2 - 5x + 6 = 0$$

Accepted Answer

$$x = 2$$ or $$x = 3$$

Answer

$$x = 1$$ or $$x = 6$$

Answer

$$x = -2$$ or $$x = -3$$

Answer

$$x = 5$$ or $$x = -6$$

Question 2

Which of the following is the correct factorization of $$x^2 + 7x + 10$$ ?

Accepted Answer

$$(x + 2)(x + 5)$$

Answer

$$(x - 2)(x - 5)$$

Answer

$$(x + 5)(x + 2)$$

Answer

$$(x - 5)(x + 2)$$

Question 3

If a quadratic equation is written in the form $$ax^2 + bx + c = 0$$ , what is the standard form?

Accepted Answer

$$ax^2 + bx + c = 0$$

Answer

$$ax + bx^2 + c$$

Answer

$$ax^2 + bx - c$$

Answer

$$a + bx + cx^2 = 0$$

Question 4

Apply the zero product property to solve: $$(x - 4)(x + 5) = 0$$

Accepted Answer

$$x = 4$$ or $$x = -5$$

Answer

$$x = -4$$ or $$x = 5$$

Answer

$$x = 4$$ or $$x = 5$$

Answer

$$x = -4$$ or $$x = -5$$

Question 5

Factor and solve: $$3x^2 - 12x = 0$$

Accepted Answer

$$x = 0$$ or $$x = 4$$

Answer

$$x = 0$$ or $$x = -4$$

Answer

$$x = 3$$ or $$x = -4$$

Answer

$$x = 3$$ or $$x = 4$$

Question 6

What is the factored form of $$x^2 - 9$$ ?

Accepted Answer

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

Answer

$$(x + 9)(x - 9)$$

Answer

$$(x - 3)^2$$

Answer

$$(x + 3)^2$$

Question 7

Solve by factoring: $$x^2 + x - 12 = 0$$

Accepted Answer

$$x = 3$$ or $$x = -4$$

Answer

$$x = -3$$ or $$x = 4$$

Answer

$$x = 12$$ or $$x = -1$$

Answer

$$x = -12$$ or $$x = 1$$

Question 8

Which of the following represents the correct factorization of $$2x^2 + 8x + 6$$ ?

Accepted Answer

$$2(x + 3)(x + 1)$$

Answer

$$2(x + 1)(x + 3)$$

Answer

$$2(x^2 + 4x + 3)$$

Answer

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

Question 9

Factor completely: $$4x^2 - 16$$

Accepted Answer

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

Answer

$$4(x^2 - 4)$$

Answer

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

Answer

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

Question 10

Solve the quadratic equation by factoring: $$2x^2 - 18 = 0$$

Accepted Answer

$$x = 3$$ or $$x = -3$$

Answer

$$x = 9$$ or $$x = -9$$

Answer

$$x = \sqrt{9}$$ or $$x = -\sqrt{9}$$

Answer

$$x = 6$$ or $$x = -6$$

Question 11

What is the factored form of $$x^2 - 16x + 64$$ ?

Accepted Answer

$$(x - 8)^2$$

Answer

$$(x - 4)(x - 16)$$

Answer

$$(x + 8)^2$$

Answer

$$(x + 4)(x + 16)$$

Question 12

Solve by factoring: $$x^2 + 6x + 9 = 0$$

Accepted Answer

$$x = -3$$

Answer

$$x = 3$$

Answer

$$x = -3$$ or $$x = 3$$

Answer

$$x = 0$$

Question 13

Which of the following is the correct factorization of $$3x^2 + 12x + 12$$ ?

Accepted Answer

$$3(x + 2)^2$$

Answer

$$3(x + 2)(x + 2)$$

Answer

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

Answer

$$3(x^2 + 4x + 4)$$

Question 14

Factor and solve: $$5x^2 - 20 = 0$$

Accepted Answer

$$x = 2$$ or $$x = -2$$

Answer

$$x = 4$$ or $$x = -4$$

Answer

$$x = \sqrt{4}$$ or $$x = -\sqrt{4}$$

Answer

$$x = 5$$ or $$x = -5$$

Question 15

What is the factored form of $$6x^2 - 24x + 18$$ ?

Accepted Answer

$$6(x - 3)(x - 1)$$

Answer

$$6(x - 1)(x - 3)$$

Answer

$$6(x^2 - 4x + 3)$$

Answer

$$6(x - 2)^2$$

Question 16

Use Factoring and the Zero Product Property to solve:

$$0=x^2+2x-15$$

Accepted Answer

x = -5

and

x = 3

Answer

x = 5

and

x = 3

Answer

x = -5

and

x=-3

Answer

x = 5

and

x = -3

Question 17

Convert x²- 9x + 20 to factored form and solve.

Accepted Answer

(x-4)(x-5); x = 4, 5

Answer

(x-10)(x+2); x = -2, 10

Answer

(x+4)(x+5); x = -5, -4

Answer

Not factorable

Question 18

Solve:
x² - 49 = 0

Accepted Answer

x = -7, x = 7

Answer

x = -7

Answer

x = 7

Answer

x = -7, x = 1

Question 19

Factor
k² - 2k - 24

Accepted Answer

(k+4)(k-6)

Answer

(k+4)(k+6)

Answer

(k+6)(k-1)

Answer

(k-4)(k+6)

Question 20

Factor Completely:
3x² + 18x +15
Hint: Factor GCF first.

Accepted Answer

3(x + 5)(x + 1)

Answer

3(x² + 6x + 5)

Answer

(x + 5)(x + 1)

Answer

Prime

Question 21

Solve $$\left(x+2\right)\left(x-11\right)=0$$ for x.

Accepted Answer

$$x=-2$$ or $$x=11$$

Answer

$$x=-2$$ or $$x=-11$$

Answer

$$x=2$$ or $$x=-11$$

Answer

$$x=2$$ or $$x=11$$

Mastering Quadratic Functions Through Factoring

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