Find the factors of polynomial functions using synthetic division. f(x) {x}^(3) + {4x}^(2) - 2x - 10a. find the factor of the polynomial b. find the zeros of the polynomial.

Question

find the factors of polynomial functions using synthetic division. f(x)
`{x}^(3) + {4x}^(2) - 2x - 10`a. find the factor of the polynomial b. find the zeros of the polynomial.

Answer 1

x^3 + 4x^2 - 2x - 10

I'll use some factors like -1, +1, -2, +2, -5, +5, -10 + 10

1 4 -2 -10 -1

-1 -3 5

1 3 -5 -5 -1 is not a factor

1 4 -2 -10 1

1 5 3

1 5 3 -7 1 is not a factor

1 4 -2 -10 2

2 12 20

1 6 10 -10 2 is not a factor

1 4 -2 -10 -2

-2 -4 12

1 2 -6 2 -2 is not a factor

1 4 -2 -10 5

5 35 165

1 9 33 155 5 is not a factor

1 4 -2 -10 -5

-5 5 -15

1 -1 3 -25 -5 is not a factor

1 4 -2 -10 -10

-10 60 -580

1 -6 58 -590

1 4 -2 -10 10

10 140 1380

1 14 138 1370 10 is not a factor

This polynomial does not have exact roots

It is not possible to use the synthetic division to solve it.

The roots are: -3.8, -1.7, 1.5