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# What is multiplicity in a polynomial?

A polynomial is an expression of more than two algebraic terms, which contains the exponential powers of a single variable.

## Answer: The number of times a given factor appears in the factored form of the equation is known as the multiplicity of the polynomial.

The discriminant of the polynomial is zero if and only if the polynomial has multiple roots.

**Explanation:**

The total number of times a known factor appears in the factored form of the equation of a polynomial is called the multiplicity of the polynomial. The zero linked with this factor, x = 3, has multiplicity 3 because the factor (x−3) occurs thrice. The x-intercept x = −2 is the repeated solution of factor (x + 2)^{3} = 0

For instance,

The quadratic (*x* + 3)(*x* – 2) has the zeroes *x* = –3 and *x* = 2, each occurring once. The eleventh-degree polynomial (*x* + 3)^{4}(*x* – 2)^{7} has the same zeroes as did the quadratic, but in this case, the *x *= –3 solution has multiplicity 4 because the factor (*x *+ 3) occurs four times (that is, the factor is raised to the fourth power) and the *x* = 2 solution has multiplicity 7 because the factor (*x* – 2) occurs seven times.

### Hence, the number of times a given factor appears in the factored form of the equation is known as the multiplicity of the polynomial.

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