The degree of the polynomial P(x) is the highest power of the polynomial P(X)
A possible formula for P(x) is [tex]P(x) =(x + 5)x^2(x - 1)^2 \\[/tex]
The given parameters are:
Roots of multiplicity 2 at x=1 and x=0
Root of multiplicity 1 at x= -5
Write out the roots
x=1 and x=0 ------- Multiplicity 2
x = -5 ------- Multiplicity 1
Equate the roots to 0
x - 1 = 0 and x = 0 ------- Multiplicity 2
x + 5= 0 ------- Multiplicity 1
Place the multiplicities as the exponents of the roots
(x - 1)^2 = 0 and x^2 = 0
(x + 5)^1 = 0
Multiply the expressions
[tex](x - 1)^2 * x^2 * (x + 5)^1 = 0 * 0 * 0[/tex]
This gives
[tex](x - 1)^2 * x^2 * (x + 5) = 0[/tex]
Rewrite as:
[tex](x + 5)x^2(x - 1)^2 = 0[/tex]
Replace 0 with P(x)
[tex]P(x) =(x + 5)x^2(x - 1)^2[/tex]
Hence, a possible formula for P(x) is [tex]P(x) =(x + 5)x^2(x - 1)^2 \\[/tex]
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