Solve the polynomial equation p(x)=x3+2x2−5x−6 . Which of the following is a factor?(1 point)

Question

Responses

x−1
x minus 1

x−3
x minus 3

x+1
x plus 1

x+2

Answer 1

To determine which of the given options is a factor of the polynomial equation, we can use synthetic division.

Using the divisor x-1, we have:

1 │ 1 2 -5 -6
└─(1)─3─(-2)─(-7)

This gives us a remainder of -7, so x-1 is not a factor of the equation.

Using the divisor x-3, we have:

3 │ 1 2 -5 -6
└─(3)─15─30─72

This gives us a remainder of 72, so x-3 is not a factor of the equation.

Using the divisor x+1, we have:

-1 │ 1 2 -5 -6
└─(1)─(-1)─6

This gives us a remainder of 6, so x+1 is not a factor of the equation.

Using the divisor x+2, we have:

-2 │ 1 2 -5 -6
└─(2)─0─10

This gives us a remainder of 10, so x+2 is not a factor of the equation.

Therefore, none of the given options (x-1, x-3, x+1, x+2) are factors of the polynomial equation p(x)=x^3+2x^2−5x−6.