Question

The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity at x=-2.
find a possible formula for P(x)
P(x)=

Answer 1

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

What are polynomials?

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

Given the roots of the polynomial, therefore, the following details can be written as,

• The polynomial has a root of multiplicity 2 at x=2, (x-2)²
• The polynomial has a root of multiplicity 2 at x=0, (x-0)²
• The polynomial has a root of multiplicity 1 at x=-2, (x+2)¹

Therefore, the polynomial will become,

P(x) = (x-2)²(x-0)²(x+2)¹

      = (x²+4-4x) (x)² (x+2)

       = (x²+4-4x) (x³+2x²)

       = x⁵ + 2x⁴ + 4x³ + 8x² - 4x⁴ -8x³

       = x⁵ - 2x⁴ - 4x³ + 8x²

Hence, the possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

Learn more about Polynomial:

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