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Answer:
P(x)=(x-2)(x-4)(x+3)(x+6)
Step-by-step explanation:
Given: P(x)=x⁴+3x³-28x²-36x+144
It is a polynomial with degree 4.
It should maximum four factor.
Hit and trial error method.
Put x = 2 into P(x)
P(2)=2⁴+3×2³-28×2²-36×2+144
P(2) = 0
So, x-2 would be factor of P(x)
Now divide x⁴+3x³-28x²-36x+144 by x-2 to get another factors
Put x = 4
now divide by x-4
Now factor
Complete factor of P(x)
P(x)=(x-2)(x-4)(x+3)(x+6)