Question

Could someone help me a little with this?
polynomial factoring related

Answer 1

Let's factor up

• 2x³+14x2+24x
• 2x(x²+7x+12)
• 2x(x²+4x+3x+12)
• 2x(x+4)(x+3)

So

• Length=2x
• Breadth=x+3
• Height=x+4

[Can be interchanged]

Answer 2

`2x(x+3)(x + 4)`

Explanation:

To factor
`2x^3+14x^2+24x`

First, factor out the common term
`2x`:

`\implies 2x(x^2+7x+12)`

Now factor the expression in the parantheses:
`x^2+7x+12`

Find two numbers that multiply to 12 and sum to 7: 3 and 4

Rewrite
`7x` as the sum of these 2 numbers:

`\implies x^2+3x + 4x+12`

Factorize the first two terms and the last two terms separately:

`\implies x(x+3) + 4(x+3)`

Factor out the common term
`(x+3)`:

`\implies (x+3)(x + 4)`

Therefore, the final factorization of the polynomial is:

`\implies 2x (x+3)(x + 4)`