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grin007 [14]
2 years ago
7

Plz help

Mathematics
1 answer:
kvv77 [185]2 years ago
8 0

Option C: 5 x(4 x+7)(3 x+2) is the possible expressions for length, width and height of the prism.

Explanation:

The volume of the rectangular prism is 60 x^{3}+145 x^{2}+70 x

To determine the length, width and height of the rectangular prism, let us factor the expression.

Thus, factoring 5x from the expression, we have,

5 x\left(12 x^{2}+29 x+14\right)

Let us break the expression 12 x^{2}+29 x+14 into two groups, we get,

5x[\left(12 x^{2}+8 x\right)+(21 x+14)]

Factoring 4x from the term 12 x^{2}+8 x , we get,

5x[4 x(3 x+2)+(21x+14)]

Similarly, factoring 7x from the term 21 x+14 , we get,

5x[4 x(3 x+2)+7(3x+2)]

Now, let us factor out 3x+2, we get,

5 x(4 x+7)(3 x+2)

Hence, the possible expressions for length, width and height of the prism is 5 x(4 x+7)(3 x+2)

Therefore, Option C is the correct answer.

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