ingathat8b9

2022-02-01

How do you write a polynomial in standard form, then classify it by degree and number of terms $2-11{x}^{2}-8x+6{x}^{2}$?

ljmolerovae

Expert

Explanation:
Standard form of polynomial equation of ${2}^{nd}$ order is
$a{x}^{2}+bx+c$
Rearrange the like terms together and then simplify. Then arrange then again rearrange them in the standard format given above.
$2-11{x}^{2}-8x+6{x}^{2}=2+\left(-11{x}^{2}+6{x}^{2}\right)-8x$
$=2-5{x}^{2}-8x=-5{x}^{2}-8x+2$
$-5{x}^{2}-8x+2$

Veschettijib

Expert

The polynomial has three terms (separated by + and - signs), and a degree of 2 because the largest exponent is 2.
Explanation:
Write in standard form:
$2-{11}^{2}-8x+6{x}^{2}$
Simplify $-{11}^{2}+6{x}^{2}$
$2-5{x}^{2}-8x$
Rearrange the terms from greatest to least exponent.
$-5{x}^{2}$: exponent of 2
-8x: exponent of 1
2: exponent of 0
$-5{x}^{2}-8x+2$
The polynomial has three terms (separated by + and -signs), and a degree of 2 because the largest exponent is 2.
Result:
$-5{x}^{2}-8x+2$

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