2022-01-29

What is the leading term, leading coefficient, and degree of this polynomial $f\left(x\right)={x}^{2}\left(\sqrt{2}\right)+x-5$?

Nevaeh Jensen

Expert

Explanation:
$f\left(x\right)={x}^{2}\left(\sqrt{2}\right)+x-5$
We can write this as:
$f\left(x\right)=\sqrt{2}{x}^{2}+x+5$
This is a quadratic in standard form: $a{x}^{2}+bx+c$
Where: $a=\sqrt{2}$, b=1 and c=5
Hence, Leading term: $\sqrt{2}{x}^{2}$ and leading coefficient: $\sqrt{2}$.
Also, a quadratic function is of degree 2, since the leading term is of x to the power 2.
Leading term $\sqrt{2}{x}^{2}$, Leading coefficient: $\sqrt{2}$, Degree 2.

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