Question

Simplify the polynomial expression and then write in standard form.
$(3+5x+7x^2+9x^3)$
$+(4+2x-3x^2-8x^3)$

• A. $7+7x+4x^2+x^3$
• B. $x^3+4x^2+7x+7$
• C. $x^3-4x^2+7x+7$
• D. $7+7x+4x^2-x^3$

Answer 1

The correct option is B $x^3+4x^2+7x+7$

Given a polynomial expression
$(3+5x+7x^2+9x^3)$
$+(4+2x-3x^2-8x^3)$

$\underset{–}{Step1:}$

Simplification by combining the like terms:
$(3+4)+(5x+2x)+(7x^2-3x^2)+$
$(9x^3-8x^3)$
$=7+7x+4x^2+x^3$

$\underset{–}{Step2:}$

Writing the expression obtained after simplification in standard form.

The term $x^3$ has the highest power of the variable $x$. This term would be the first term in standard form of the polynomial $7+7x+4x^2+x^3$.

The term $4x^2$ has the second highest power of the variable $x$. This term would be the second term in standard form of the polynomial $7+7x+4x^2+x^3$.

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 $7+7x+4x^2+x^3$.

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 $7+7x+4x^2+x^3$.

The standard form of the polynomial $7+7x+4x^2+x^3$ would be:
$x^3+4x^2+7x+7$

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