Question

use the factor theorem to find if g(x)is a factor of f(x)​

Answer 1

Solution:

Given f(x) = x³-6x²+11x-6

g(x) = x²-3x+2

= x²-1x-2x+2

/* splitting the middle term */

= x(x-1)-2(x-1)

= (x-1)(x-2)

i) If f(x) is divided by (x-1)

the remainder f(1)

f(1) = 1³-6(1)²+11(1)-6

= 1-6+11-6

= 12-12

=0

Therefore,

(x-1) is a factor of f(x).

ii) if f(x) divided by (x-2) the

remainder is f(2)

f(2) = 2³-6(2)²+11(2)-6

= 8 - 24+22-6

= 30-30

= 0

Therefore,

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

Now ,

we conclude that,

(x-1),(x-2) are factors of f(x).

So, (x-1)(x-2) =g(x) is a factor of f(x)

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