Math CentralQuandaries & Queries


Question from Susan, a parent:

Write the polynomial P(x)=x^3-3x^4+17x+11-4/3x^2 in descending order. Identify the leading term and the leading coefficient.

Hi Susan,

Let me illustrate with a different polynomial, Q(x) = 4x - 4/3 x2 + 3 x5 + x4 - 12.

Writing the polynomial in descending order means in order of decreasing powers. The highest power of x in this polynomial is x5 so I start with the x5 term and then the x4 term then the x3 term and so on. Thus I get

Q(x) = 3 x5 + x4 - 4/3 x2 + 4x - 12.

The leading term is the term with the highest power of x so it's 3 x5. The leading coefficient is the coefficient of the leading term so it's 3.

I hope this helps,

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