Write this as a polynomial in standard form (by factoring out 2 \pi ). 2\pi(x^2 + 4x + 4) +...

Question:

Write this as a polynomial in standard form (by factoring out {eq}2 \pi {/eq}).

{eq}2\pi(x^2 + 4x + 4) + 2\pi(x^2 + 7x + 10) {/eq}

Polynomial:

A polynomial is said to be in the standard form if the highest degree term is the first term, the second-highest degree term is the second term and so on.

Answer and Explanation:

The given expression is:

$$\begin{align} 2\pi(x^2 + 4x + 4) + 2\pi(x^2 + 7x + 10) &= 2\pi(x^2 + 4x + 4+x^2 + 7x + 10) & [ \text{Factored out }2\pi ]\\[0.5cm] &= 2\pi (2x^2+11x+14) & [ \text{Like terms are combined} ]\\[0.5cm] &= \boxed{\mathbf{4\pi x^2 +22\pi x+ 28\pi}} & [2\pi \text{ is distributed} ] \end{align} $$


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