Question

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

Answer 1

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

$(x^4+3x^3-28x^2-36x+144)\div (x-2) = x^3+5x^2-18x-72$

$P(x)=(x-2)(x^3+5x^2-18x-72)$

Put x = 4

$P(4) = 0$

now divide $x^3+5x^2-18x-72$ by x-4

$(x^3+5x^2-18x-72)\div (x-4) = x^2+9x+18$

$P(x)=(x-2)(x-4)(x^2+9x+18)$

Now factor $x^2+9x+18$

$\Rightarrow x^2+9x+18$

$\Rightarrow (x+6)(x+3)$

Complete factor of P(x)

P(x)=(x-2)(x-4)(x+3)(x+6)