SOLUTION: True or false. The polynomial {{{x^2 - 7x + 5}}} has a degree of two.

Algebra ->  Expressions-with-variables -> SOLUTION: True or false. The polynomial {{{x^2 - 7x + 5}}} has a degree of two.       Log On


   



Question 141321: True or false.
The polynomial x%5E2+-+7x+%2B+5 has a degree of two.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
True or false.
The polynomial x%5E2+-+7x+%2B+5 has a degree of two.

The degree of a polynomial is the maximum number of variables
(letters) that are multiplied together in any one term of
the polynomial.

x%5E2+-+7x+%2B+5 means

xx+-+7x+%2B+5

and there are two variables (letters), both x's,
which are multiplied together in the first 
term "xx".  So the degree is 2.

Since there is only one letter in the polynomial
you merely have to pick out the largest exponent.

-----------------------

If you had this polynomial

4x%5E2y%5E4-7x%5E3%5Ey%5E4%2B11x%5E4%2B5xy%5E5+%2B+2y+%2B+5

You would think of it as

4xxyyyy-7xxxyyyy%2B11xxxx%2B5xyyyyy%2B2y%2B5

The longest string of letters multiplied 
together is in the middle term which has 
this longest string of letters xxxyyyy.
That consists of 7 letters multiplied
together, so the degree is 7.

It's easy to see that you don't have to
string the letters out like I did above to
see how many are multiplied together,
you can just add the exponents of the
letters and pick the biggest sum.

Edwin