Question

Find the least common multiple (LCM) of 2x^4 – 6x^3 – 8x^2 and 4x^3 – 4x.

You can give your answer in its factored form.

Answer 1

The least common multiple (LCM) of the expression 2x⁴ - 6x³ - 8x² and 4x³ - 4x is 4x²(x - 1)(x + 1)(x - 4)

Finding the least common multiple (LCM) of the expression

From the question, we have the following parameters that can be used in our computation:

2x⁴ - 6x³ - 8x² and 4x³ - 4x.

When the expressions are factored, we have

2x²(x² - 3x - 4) and 4x(x² - 1)

Next, we have

2x²(x - 4)(x + 1) and 4x(x - 1)(x + 1)

Simplify further

2 * x * x(x - 4)(x + 1) and 2 * 2 * x(x - 1)(x + 1)

Using the above as a guide, we take the product of the all factors without repetition as the LCM

So, we have

LCM = 2 * 2 * x * x * (x + 1) * (x - 1) * (x - 4)

Evaluate

LCM = 4x²(x - 1)(x + 1)(x - 4)

Hence, the least common multiple (LCM) of the expression is 4x²(x - 1)(x + 1)(x - 4)

Answer 2

Explanation:

`\underline{ \underline{ \text{Solution}}} :`

`\text{1. \: First \: expression} : \tt{2 {x}^(4) - 6 {x}^(3) - 8 {x}^(2) }`

⤑
`\tt{2 {x}^(2)( {x}^(2) - 3x - 4) }`

⤑
`\tt{2 {x}^(2) \{ \: {x}^(2 ) - \: (4 - 1)x - 4 \} }`

⤑
`\tt{2 {x}^(2) \{ {x}^(2) - 4x + x - 4 \} }`

⤑
`\tt{2 {x}^(2) \{ x(x - 4) + 1(x - 4) \} }`

⤑
`\tt{2 {x}^(2) (x - 4)(x + 1)}`

`\text{2. Second \: expression} : \tt{4 {x}^(3) - 4x }`

⤑
`\tt{4x( {x}^(2) - 1)}`

⤑
`\tt{4x(x + 1)(x - 1)}`

L.C.M = Common × Remaining

= ( x + 1 ) × ( x - 1 ) × ( x - 4 ) × 2x² × 4x

= 8x³ ( x + 1 ) ( x - 1 ) ( x - 4 )

`\red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt \: 8 {x}^(3) (x + 1)(x - 1)(x - 4)}}}}}}`

Hope I helped !

Have a wonderful day / night !

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