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andrew-mc [135]
3 years ago
11

How do you write polynomials in standard form

Mathematics
2 answers:
andre [41]3 years ago
6 0
You put the highest exponent power first, then you go down until you reach a regular number (a number with a variable goes before a normal number)

Ex: 5x^3+2x^2+4x+5
kenny6666 [7]3 years ago
5 0

One way to write a polynomial is in standard form. In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write.


Let’s look at an example.


Write the expression 3x−8+4x5 in standard form.


First, look at the degrees for each term in the expression.


3x has a degree of 1


8 has a degree of 0


4x5 has a degree of 5


Next, write this trinomial in order by degree, highest to lowest


4x5+3x−8


The answer is 4x5+3x−8.


The degree of a polynomial is the same as the degree of the highest term, so this expression is called a fifth degree trinomial.

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Please help me with 2b ASAP. <br> Really appreciate it!!
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f(x)=\dfrac{x^2}{x^2+k^2}

By definition of the derivative,

f'(x)=\displaystyle\lim_{h\to0}\frac{\frac{(x+h)^2}{(x+h)^2+k^2}-\frac{x^2}{x^2+k^2}}h

f'(x)=\displaystyle\lim_{h\to0}\frac{(x+h)^2(x^2+k^2)-x^2((x+h)^2+k^2)}{h(x^2+k^2)((x+h)^2+k^2)}

f'(x)=\dfrac{k^2}{x^2+k^2}\displaystyle\lim_{h\to0}\frac{(x+h)^2-x^2}{h((x+h)^2+k^2)}

f'(x)=\dfrac{k^2}{x^2+k^2}\displaystyle\lim_{h\to0}\frac{2xh+h^2}{h((x+h)^2+k^2)}

f'(x)=\dfrac{k^2}{x^2+k^2}\displaystyle\lim_{h\to0}\frac{2x+h}{(x+h)^2+k^2}

f'(x)=\dfrac{2xk^2}{(x^2+k^2)^2}

\dfrac{k^2}{(x^2+k^2)^2} is positive for all values of x and k. As pointed out, x\ge0, so f'(x)\ge0 for all x\ge0. This means the proportion of occupied binding sites is an increasing function of the concentration of oxygen, meaning the presence of more oxygen is consistent with greater availability of binding sites. (The question says as much in the second sentence.)

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This is  a true statement

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