Consider the polynomial p(x)=x⁴+3x³-28x²-36x+144. write the equation of p in factored form.

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)

correct answers below: