17. Factorise using factor theorem:
x^3-3x^2-4x+12

(x - 3)(x - 2)(x + 2)

Step-by-step explanation:

Given

x³ - 3x² - 4x + 12 ( factor the first/second and third/fourth terms )

= x²(x - 3) - 4(x - 3) ← factor out (x - 3) from each term

= (x - 3)(x² - 4) ← x² - 4 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 4

= x² - 2²

= (x - 2)(x + 2)

Thus

x³ - 3x² - 4x + 12 = (x - 3)(x - 2)(x + 2) ← in factored form

(x - 2)(x - 3)(x + 2).

Step-by-step explanation:

The Factor Theorem states that if x - a is a factor of f(x) the f(a) = 0.

f(x) = x^3 - 3x^2 - 4x + 12

We try the factors of 12:

f(2) =  2^3 - 3*4 - 8 +12

= 8 - 12 - 8 + 12  = 0

- so (x - 2) is a factor of f(x)

Dividing:

        x^2  -  x -  6            <Quotient

x - 2 )x^3 - 3x^2 - 4x + 12

        x^3 - 2x^2

                  -x^2 - 4x

                  -x^2 + 2x

                          -6x + 12

                          -6x + 12

So we factor x^2 - x - 6:

= (x - 3)(x + 2)

answer: 1 and 3

step-by-step explanation:

step-by-step explanation: