Question

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from 20 of this month is my exam ​

Answer 1

Answer:

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Answer 2

Factorisation of polynomial is done as :

$4 {x}^{3} - 28 {x}^{2} + 48x \\ = > 4x( {x}^{2} - 7x + 12) \\ = > 4x( {x}^{2} - 4x - 3x + 12) \\ = > 4x[x(x - 4) - 3(x + 4)] \\ = > (4x)(x - 4)(x - 3 )$

Now, the factorization shown above is simplest factorization done with X terms.. which can be further rearranged like multiplication of terms by (-) or further factorization of (4x) or breaking down (4x) and multiplying it to remaining factors etc.

Now, Let say a square of side $x$ is cut from each corner and then box is made..

Then,

Length of Box = (8-x-x) = 8-2x

Width of Box = (6-x-x) = 6-2x

Height of box = Size of square cut = x

So,$Volume = (8-2X)(6-2X)(X)$

& rearranging factors we get,

$(4x)(x - 4)(x - 3) \\ = > (2)(2)(x)( - )( - )(x - 4)(x - 3) \\ = > (x)[( - )(2)(x - 4)][( - )(2)(x - 3) ]\\ = > (x)(8 - 2x)(6 - 2x) \\ = > (8 - 2x)(6 - 2x)(x)$

So, we can see that Volume calculated And factorization of polynomial is same..

Hence, We can conclude that volume of the BOX is EQUIVALENT to the POLYNOMIAL.