Question

use factor theorem in each of the following

Answer 1

1) x= 3
f(x) = 3^3-6(3)^2+11(3)-6
= 27-54+33-6
=0
2) x= -1
f(x)= 2(-1)^3-9(-1)^2+(-1)+12
= -2-9-1+12
= 0
they are the zeroes of the polynomial

Answer 2

HEYA......

1. g(x) = x - 3
=> x - 3 = 0
=> x = 3

f(x) =x^3 - 6x^2 + 11x - 6
= 3^3 - 6*3^2 + 11*3 - 6
= 27 - 54 + 33 - 6
= 60 - 60
= 0

Here remainder is 0 so g(x) is a factor of f(x).

2. g(x) = x + 1
=> x + 1 = 0
=> x = -1

f(x) = 2x^3 - 9x^2+ x +12
= 2*(-1)^3 - 9*(-1)^2 + (-1) + 12
= (-2) - 9 + (-1) +12
= -2 - 9 - 1 +12
= - 11 + 11
= 0

Here remainder is 0 so g(x) is a factor of f(x)

3. g(x) = x√2
=> x√2 = 0
=> x = -√2

f(x) = 7x^2 - 2√8x - 6
= 7*(-√2)^2 - 2*√8*(-√2) - 6
= 7*2 - 2*√-16 - 6
= 14 - 2*(-4) - 6
= 14 + 8 - 6
= 22 - 6
= 16

Here remainder is not 0 so g(x) is not a factor of f(x).