To Express q(x)=12x^5+40x^4-32x^3 in the form described in the Linear Factorization Theorem. The zero is 0, 2/3, -4 and the multiplicity is: 3, 1, 1.
Factorization
q(x)=12x^5+40x^4-32x³
q(x)=4x³ (3x²+10x-8)
q(x)=4x³(3x²+12x-2x-8)
q(x)=4x³ [(3x (x+4)-2 (x+4)]
q(x)=4x³ (3x-2) (x+4)
When:
q(x)=0; x1=0; x2=2/3; x3=-4
Hence:
When:
x=0 the multiplicity is 3
x=2/3 the multiplicity is 1
x=-4 the multiplicity is 1
Therefore the zero is 0, 2/3, -4 and the multiplicity is: 3, 1, 1.
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