What is the quotient (125 - 8x³) ÷ (25 + 10x + 4x²)?
-2x + 5, 2x - 5, -2x - 5, 2x + 5

Solution:

We will factorise the 125 - 8x³ using the algebraic identity (a)³ - (b)³ = (a - b)(a² + ab + b²)

125 - 8x³ can be expressed in the factored form.

(5)³ - (2x)³ = (5 - 2x)(25 + 10x + 4x²)

To find the quotient when (125 - 8x³) ÷ (25 + 10x + 4x²), we will divide them by the factors.

(5 - 2x)(25 + 10x + 4x²) / (25 + 10x + 4x²)

Cancel the terms, to get the quotient

(5 - 2x) or (-2x + 5) is the quotient.

What is the quotient (125 - 8x³) ÷ (25 + 10x + 4x²)?

Summary:

The quotient when (125 - 8x³) ÷ (25 + 10x + 4x²) is (5 - 2x) or (- 2x + 5).