Show that (x + 4), (x – 3) and (x – 7) are factors of x3 – 6x2 �

1.	Show that (x + 4), (x – 3) and (x – 7) are factors of x3 – 6x2 – 19x + 84
Answer» Let f(x) = x³ – 6x² – 19x + 84 To verify whether (x + 4), (x – 3) and (x – 7) are factors of f(x) we use factor theorem. Let f(- 4), f(3) and f(7) f(- 4) = (- 4)³ – 6 (- 4)² – 19 (- 4) + 84 = -64 – 96 + 76 + 84 = 0 . ∴ (x + 4) is a factor of f(x). f(3) = 3³ – 6(3)² – 19(3) + 84 = 27 – 54 – 57 + 84 = 0 ∴ (x – 3) is a factor of f(x). f(7) = 7³ – 6(7)² – 19(7) + 84 = 343 – 294 – 133 + 84 = 427 – 427 = 0 ∴ (x – 7) is a factor of f(x).

Show that (x + 4), (x – 3) and (x – 7) are factors of x3 – 6x2 – 19x + 84

Answer»

Let f(x) = x³ – 6x² – 19x + 84

To verify whether (x + 4), (x – 3) and (x – 7) are factors of f(x) we use factor theorem.

Let f(- 4), f(3) and f(7)

f(- 4) = (- 4)³ – 6 (- 4)² – 19 (- 4) + 84

= -64 – 96 + 76 + 84 = 0 .

∴ (x + 4) is a factor of f(x).

f(3) = 3³ – 6(3)² – 19(3) + 84

= 27 – 54 – 57 + 84

= 0

∴ (x – 3) is a factor of f(x).

f(7) = 7³ – 6(7)² – 19(7) + 84

= 343 – 294 – 133 + 84

= 427 – 427 = 0

∴ (x – 7) is a factor of f(x).