What polynomial identity should be used to prove that 162 = (10 + 6)2?

Question

mathstudent55 · Answer

The 2's are exponents, right?

mathstudent55 · Answer

The square of a binomial:

$(a + b)^2 = a^2 + 2ab + b^2$

anonymous · Answer

yes

anonymous · Answer

i understand that but i just need to know if i have the right answer

mathstudent55 · Answer

Use a = 10 and b = 6.
Substitute those values in for those variables, and evaluate it.

anonymous · Answer

so would the answer be Square of Binomial

mathstudent55 · Answer

$(a + b)^2 = a^2 + 2ab + b^2 $

$(10 + 6)^2 = 10^2 + 2 \times 10 \times 6 + 6^2$

Now that all you have is numbers, and no more variables, calculate each side.

anonymous · Answer

is it square of binomial

mathstudent55 · Answer

Yes. If all you need to do is identify the polynomial identity, that's it.
If you need to show how it works, then continue to evaluate both sides of the expression above.

anonymous · Answer

i have anotheer question

anonymous · Answer

What is the end behavior of the function f(x) = 3x4-x3 + 2x2 + 4x + 5? @mathstudent55

mathstudent55 · Answer

The highest degree term in this polynomial is which term?

anonymous · Answer

5?

mathstudent55 · Answer

No.
The degree of a polynomial is the highest exponent (or sum of exponents) of all terms of the polynomial.

mathstudent55 · Answer

The first term is 3x^4.
The degree of the polynomial is 4.

anonymous · Answer

ok

anonymous · Answer

so is it Up on the left, down on the right

mathstudent55 · Answer

Now think of a number raised to the 4th power.
When x is negative, and getting more negative, as it approaches negative infinity, what happens to x^4?

anonymous · Answer

so am i right

mathstudent55 · Answer

Not so fast. We haven't looked at when x is positive and approaches positive infinity.

mathstudent55 · Answer

Once again, 
When x is negative, and getting more negative, as it approaches negative infinity, what happens to x^4?

anonymous · Answer

it goes down

anonymous · Answer

so am i right

mathstudent55 · Answer

If you take a negative number and raise it to the 4th power, what do you get?

anonymous · Answer

Up on the left, up on the right

 Up on the left, down on the right

 Down on the left, up on the right

 Down on the left, down on the right

anonymous · Answer

i have to go soon so can you tell me which ones right

mathstudent55 · Answer

As the x gets closer to negative infinity, what happens to $x^4$?

$(-1)^4 = 1$

$(-2)^4 = 16$

$(-3)^4 = 81$

$(-4)^4 = 256$

$(-10)^4 = 10,000$

anonymous · Answer

please i need to go soon

mathstudent55 · Answer

It gets larger.
The same thing happens when x gets closer to positive infinity.
x^4 gets larger.

The graph of this polynomial will look like this:

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