Write a polynomial of degree 3 in the variable x, in which the coefficient of the x² term is –7.
Polynomials
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Question

Write a polynomial of degree 3 in the variable x, in which the coefficient of the x2 term is –7.

KnowledgeBoat · Accepted Answer

A polynomial of degree 3 has its highest power of the variable as 3.

The general form of such a polynomial is ax³ + bx² + cx + d, where a ≠ 0.

Here, the coefficient of x² is given to be -7.

So, b = -7.

We may choose any non-zero value for a (the coefficient of x³) and any values for c and d.

For example, taking a = 1, c = 5 and d = 2, we get:

Polynomial: x³ - 7x² + 5x + 2

(Note: Many other polynomials are also possible, such as 2x³ - 7x² + 4, 3x³ - 7x² - x + 1, etc.)

Mathematics