Question

The cubic polynomial x^3-2x^2-2x+4 has a factor of (x-a) where a is an integer.
Use the factor theorem to find a

Answer 1

If (x-a) is a factor of f(x), then f(a) = 0. Use this fact to find 'a'.

Answer 2

(x-a) is a factor of x^3-2x^2-2x+4. That implies f(a) = 0.
Therefore, a^3 - 2a^2 - 2a + 4 = 0.
If you know the rational roots theorem, you can use that to find potential roots, try each one until a^3 - 2a^2 - 2a + 4 = 0.

Answer 3

yes i did reach to A63-2a^2-2a+4=0

Answer 4

Do you know rational roots theorem?

Answer 5

sorry a^3

Answer 6

no to be honest.

Answer 7

i could search it up on google

Answer 8

Take the constant term and write down all its factors.
Take the leading coefficient and write down all its factors.
Then the possible roots are all possibilities of the first divided by the second.

Answer 9

Constant term is 4. Possible factors are: 1, 2, 4
Leading coefficient is: 1. This has only one factor: 1
Possible roots are: \(\Large \pm\frac{1,2,4}{1}\)

Answer 10

Try a = +1, -1, +2, -2, +4, -4 until you find one of them that makes the equation equal to zero. That will be your 'a' value.