Respuesta :

Answer:

Option A

Step-by-step explanation:

Given expression:

  • 3x² - 10x - 8

Option A

⇒ (x - 4)(3x + 2)

⇒ (x × 3x) + (2 × x) + (-4 × 3x) + (-4 × 2)

⇒ (3x²) + (2x) + (-12x) + (-8)

⇒ 3x² + 2x - 12x - 8

⇒ 3x² - 10x - 8

3x² - 10x - 8 = 3x² - 10x - 8 (Yes!)

Option B

⇒ (3x - 4)(x - 2)

⇒ (3x × x) + (3x × -2) + (-4 × x) + (-4 × -2)

⇒ (3x²) + (-6x) + (-4x) + (8)

⇒ 3x² - 6x - 4x + (8)

⇒ 3x² - 10x + 8

3x² - 10x - 8 = 3x² - 10x + 8 (No!)

Option C

⇒ (3x - 4)(x + 2)

⇒ (3x × x) + (3x × 2) + (-4 × x) + (-4 × 2)

⇒ (3x²) + (6x) + (-4x) + (-8)

⇒ 3x² + 6x - 4x - 8

⇒ 3x² + 2x - 8

3x² - 10x - 8 = 3x² + 2x - 8 (No!)

Option D

⇒ (3x - 2)(x - 4)

⇒ (3x × x) + (3x × -4) + (-2 × x) + (-2 × -4)

⇒ (3x²) + (-12x) + (-2x) + (8)

⇒ 3x² - 12x - 2x + 8

⇒ 3x² - 14x + 8

3x² - 10x - 8 = 3x² - 14x + 8 (No!)

Since the expression of option A has the same value as the given expression, option A is correct.

lovebelt

Answer:

Hi! Let's find which expression is equivalent to [tex]3x^{2} - 10x - 8[/tex]. First, remember that expressions are equivalent when they have identical solutions or roots. That means we have to do three things:

- solve [tex]3x^{2} - 10x - 8[/tex]

- review the listed expressions

- determine which solution is equivalent to the solution of [tex]3x^{2} - 10x - 8[/tex]

First, let's solve [tex]3x^{2} - 10x - 8[/tex].

Use the sum-product pattern -

3x^2 - 10x - 8

3x^2 + 2x - 12x - 8

Common factor from the two pairs -

3x^2 + 2x - 12x - 8

x(3x + 2) - 4(3x + 2)

Rewrite in factored form -

x(3x + 2) - 4(3x + 2)

(x - 4)(3x + 2)

Now, let's review the listed expressions. We have:

A. (x - 4)(3x + 2)

B. (3x - 4)(x - 2)

C. (3x - 4)(x + 2)

D. (3x - 2)(x + 4)

We're looking for one of these expressions to be equivalent to the solution of [tex]3x^{2} - 10x - 8[/tex], which we know is (x - 4)(3x + 2). The first choice, A. (x - 4)(3x + 2), would be our answer!

I hope this helps you. Have a wonderful day and let me know if I can help you with anything else! =)