For example, mathematicians recently discovered a way to expand it to these kinds of polynomials.

例如，数学家最近发现了一个展开这种多项式的方法。

In algebra, his work expanded our understanding of polynomial equations, opening new doors of exploration in complex numbers.

在代数方面，他的工作扩展了我们对多项式方程的理解，打开了探索复数的新大门。

Polynomials could also be used to approximate logarithmic and trigonometric functions, which are a real hassle to calculate by hand.

多项式也可以用于近似对数和三角函数这些函数手算相当麻烦。

Charles Babbage proposed a new mechanical device called the Difference Engine, a much more complex machine that could approximate polynomials.

Charles Babbage提出了一种称为差分机的新型机械装置这是一个可以近似多项式的更加复杂的机器。

The only roots of that polynomial are the imaginary numbers I and negative eye.

那个多项式的根只有虚数I和负眼。

Polynomials describe the relationship between several variables - like range and air pressure, or amount of pizza Carrie Anne eats and happiness.

多项式描述了几个变量之间的关系 例如射程和大气压力，或者Carrie Anne要吃多少披萨才会开心。

And these don’t have to be straight lines; they can be polynomials or some other fancy mathematical function.

这些不一定是直线；它们可以是多项式或其他一些奇特的数学函数。

Let's limit ourselves to polynomials, things like X squared plus three, X plus five or four x.

让我们把自己限制在多项式上 比如X²+3 x+5 4X。

Since our polynomials can have arbitrarily large degree, this set of basis functions is infinite.

由于多项式可以有任意大的阶 所以这组基函数是无限的。

But it turned out that the polynomial had a lot of symmetry and I could then exploit that symmetry to deduce all the roots.

但事实证明，这个多项式有很多对称性，我可以利用这种对称性推导出所有的根。