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Question

Simplify the polynomial expression and then write in standard form.
(3+5x+7x2+9x3)
+(4+2x−3x2−8x3)

A
7+7x+4x2+x3
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B
x3+4x2+7x+7
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C
x34x2+7x+7
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D
7+7x+4x2x3
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Solution

The correct option is B x3+4x2+7x+7
Given a polynomial expression
(3+5x+7x2+9x3)
+(4+2x3x28x3)

Step 1:––––––

Simplification by combining the like terms:
(3+4)+(5x+2x)+(7x23x2)+
(9x38x3)
=7+7x+4x2+x3

Step 2:––––––

Writing the expression obtained after simplification in standard form.

The term x3 has the highest power of the variable x. This term would be the first term in standard form of the polynomial 7+7x+4x2+x3.

The term 4x2 has the second highest power of the variable x. This term would be the second term in standard form of the polynomial 7+7x+4x2+x3.

The term 7x has the third highest power of the variable x. This term would be the third term in standard form of the polynomial 7+7x+4x2+x3.

The term 7 has the fourth highest power of the variable x, i.e., 0. This term would be the fourth term in standard form of the polynomial 7+7x+4x2+x3.

The standard form of the polynomial 7+7x+4x2+x3 would be:
x3+4x2+7x+7

Therefore, option (b.) is the correct answer.

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