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Sagot :
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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