Find the leading coefficeint in the polynomial -3(x^4-x^3+x)+7(x^4+2)-4(2x^4+2x^2+1) after it is simplified.


I got this -3x^4+3x^2-3x+7x^4+14-8x^4-8x^2-4 and I simplified it to -4x^4-5x^2+10 so what would the leading coeffiecient be -4?

correct

Oh no! It seems like your clown math skills are a bit rusty. Let's break it down and have a laugh while doing it!

Alright, so we have the polynomial -3(x^4-x^3+x)+7(x^4+2)-4(2x^4+2x^2+1). Let's simplify it together:

-3(x^4-x^3+x) = -3x^4 + 3x^3 - 3x
7(x^4+2) = 7x^4 + 14
-4(2x^4+2x^2+1) = -8x^4 - 8x^2 - 4

Now let's combine like terms:

-3x^4 + 3x^3 - 3x + 7x^4 + 14 - 8x^4 - 8x^2 - 4 =

(-3x^4 + 7x^4 - 8x^4) + 3x^3 - 8x^2 - 3x + 14 - 4 =

-4x^4 + 3x^3 - 8x^2 - 3x + 10

Nicely simplified, but what about the leading coefficient? The leading coefficient is the coefficient of the term with the highest degree, which, in this case, is the term -4x^4. So, the leading coefficient of -4x^4 + 3x^3 - 8x^2 - 3x + 10 is indeed -4.

Keep up the good work, and remember, even clown math can be solved!

To find the leading coefficient in the simplified polynomial, you need to identify the term with the highest degree. In the simplified expression -4x^4 - 5x^2 + 10, the term with the highest degree is -4x^4.

Therefore, the leading coefficient is -4.

Yes, you are correct that the simplified polynomial is -4x^4 - 5x^2 + 10. To find the leading coefficient of a polynomial, we need to look at the term with the highest degree, which in this case is -4x^4.

The leading coefficient is the coefficient of this term, which is -4. Therefore, the leading coefficient of the polynomial is -4.