Question

Show that 3x-2 is a factor of 3x^3 +x^2-20 x +12

Answer 1

Step-by-step explanation:

Let g(x) = 3x- 2 & p(x) = 3x^3+x^2-20x+12

If g(x) is an factor of p(x), then It will leave reaminder = 0 when divided.

g(x)=0

3x -2 =0

=>3x=2

=>x=2/3

Then,p(2/3) = 0 If g(x) is an factor of p(x).

p(x)=3x^3+x^2-20x+12

=>p(2/3)= 3 × (2/3)^3 + (2/3)^2 -20 × 2/3 +12

=>p(2/3)=8/9 + 4/9 -40/3 +12

=>p(2/3)= (8+4-120+108)/9

=>p(2/3)= 0/9

=>p(2/3)= 0

So,P(x) equal to 0 .

Hence,g(x) is an factor of p(x)

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