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

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Answer 1 · 2017-10-17T02:33:29

# -5x^2 -8x +2#

Standard form of polynomial equation of #2^(nd)# order is
#ax^2+bx+c#

Rearrange the like terms together and then simplify. Then arrange then again rearrange them in the standard format given above.

#2-11x^2-8x+6x^2 = 2+(- 11x^2+6x^2) -8x#
#= 2 -5x^2-8x = -5x^2 -8x +2#

Answer 2 · 2017-10-17T02:35:34

#-5x^2-8x+2#

The polynomial has three terms (separated by #+# and #-# signs), and a degree of #2# because the largest exponent is #2#.

Write in standard form:

#2-11^2-8x+6x^2#

Simplify #-11^2+6x^2#.

#2-5x^2-8x#

Rearrange the terms from greatest to least exponent.

#-5x^2: "exponent of"# #2#

#-8x":##"exponent of"# #1#

#2":##"exponent of"# #0#

#-5x^2-8x+2#

The polynomial has three terms (separated by #+# and #-# signs), and a degree of #2# because the largest exponent is #2#.

Answer 3 · 2017-10-17T02:38:54

#-5x^2-8x+2#
A polynonial of degree 2 with 3 terms also known as a "quadratic function"

#f(x) = 2-11x^2-8x+6x^2#

Combine like powers of #x# and order terms accordingly.

#f(x) =(-11+6)x^2-8x+2#

#=-5x^2-8x+2#

The degree of the polynomial is the highest power of #x#. In this case #x^2#.

#:. f(x)# is a polynomial of degree 2

#f(x)# has three terms. #[-5x^2, -8x, +2]#

NB: Such a function is also known as a "quadratic" (from the Latin word for square "quadratum")