Question

Q.19 Use the Factor Theorem to determine whether g (x) is a factor of p (x) in each of
the following cases
(i) p (x)= 2x3 +4 x2 - 2x - 1, g(x) = x - 1
(ii) p(x)= x3 + 3x2 + 3x + 10, g (x) = x-3​

Answer 1

Answer:

(i) Apply factor theorem

x+1=0

So x=−1

2x ^3 +x ^2 −2x−1

Replace x by −1, we get

2(−1) ^3 +(−1) ^2 −2(−1)−1=−2+1+2−1=0

Reminder is 0 so that x+1 is a factor of 2x ^3

+x ^2 −2x−1

(ii) Apply factor theorem

x+2=0

So x=−2

x -3 +3x -2+3x+1

Replace x by −2, we get

(−2)^3 +3(−2)^2 +3(−2)+1=−8+12−6+1=1

Reminder is 1 so that x+2 is not a factor of x -3

+3x^2 +3x+1