Question

(rx + 2)(8x^2 - 64) + 16(x^2 + 8) simplifies to -40x^3 + 32x^2 + 320x. What is the value of r?

A) -5
B) 5
C) 40
D) -40

Answer 1

The value of r in the expression can be determined by comparing the coefficient in front of the x³ term after expansion with the given simplified version of the expression. The result shows that r equals -5, which is option A.

Step-by-step explanation:

To find the value of r in the expression (rx + 2)(8x² - 64) + 16(x² + 8), we should first simplify it and compare the result to the given simplified expression of -40x³ + 32x² + 320x. The first part can be expanded as follows:

• 8rx³ - 64rx + 16x² - 128

And the second part is:

• 16x² + 128

Adding both parts gives us:

• 8rx³ + 32x² - 64rx + 320x

Comparing this to the given simplified expression, the x³ term helps us identify the value of r. For the expressions to be equivalent, 8r must equal -40, hence:

• r = -40 / 8 = -5

Therefore, the value of r is -5, which corresponds to option A.