Select the quadratic equation that is equivalent to: the product of eight and a number squared, minus the product of three and the same number is twenty-six. (1 point)

Question

Responses

3x2−8x=26
3 x squared minus 8 x is equal to 26

8x2+3x=26
8 x squared plus 3 x is equal to 26

8x2−3x=26
8 x squared minus 3 x is equal to 26

8x2−3x+26

Answer 1

Let's break down the given statement: "the product of eight and a number squared, minus the product of three and the same number is twenty-six."

Let \( x \) be the number in question.

1. The product of eight and a number squared is \( 8x^2 \).

2. The product of three and the same number is \( 3x \).

3. The equation states that the first expression minus the second expression is equal to twenty-six:

   \[ 8x^2 - 3x = 26 \]

To form a quadratic equation where all terms are on one side, we can rearrange it:

\[ 8x^2 - 3x - 26 = 0 \]

But among the given responses, the form that matches directly is:

8x² - 3x = 26

So the correct response is:

8x² - 3x = 26