Question

Select all polynomials that have (x-3) as a factor.

1. a(x) = x^3 - 2x^2 - 4x + 3
2. b(x) = x^3 + 3x^2 - 2x - 6
3. c(x) = x^4 - 2x^3 -27
4. d(x) = x^4 -20x - 21

Answer 1

Below.

Explanation:

Substitute x = 3 into each polynomial and see if the value of the polynomial is zero. If it is zero then x-3 is a factor.

Try number 1:

a(x) = x^3 - 2x^2 - 4x + 3

a(3) = 3^3 - 2(3)^2 - 4(3) + 3

= 27 - 2(9) - 12 + 3

= 27 - 18 - 12 + 3

= 9 - 18 - 9

= 27 - 27

= 0

So a(x) has (x-3) is a factor of a(x)

The other 3 polynomials are solved in the same way.