Question

The factorization of 8x3 – 125 is (2x – 5)(jx2 + kx + 25). What are the values of j and k?

j = 6 and k = –10
j = 8 and k = 10
j = 4 and k = 25
j = 4 and k = 10

Answer 1

j = 4

k = 10

Explanation:

Given expression:

8x³ - 125

• 8 is a perfect cube of 2.
• 125 is a perfect cube of 5

So, we can factorize the expression as:

= (2x)³ - (5)³

Using formula:

• a³ - b³ = (a - b)(a² + ab + b²)

In the above expression, a = 2x, b = 5

So, by substituting a and b in the above formula, we get:

= (2x - 5)[(2x)² + (2x)(5) + (5)²]

Simplify

= (2x - 5)(4x² + 10x + 25)

Comparing it with the given:

= (2x - 5)(jx² + kx + 25)

We get:

j = 4

k = 10

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