Question

Without actual division prove that (x+1) is a factor of 2x³ +x² -2x-1. Also factorise completely​

Answer 1

(i) Apply factor theorem 

x+1=0

So x=−1

2x3+x2−2x−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 2x3+x2−2x−1  

(ii) Apply factor theorem 

x+2=0 

So x=−2 

x3+3x2+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 x3+3x2+3x+1

Answer 2

Answer:

$\large\sf{Question}$

Without actual division prove that (x+1) is a factor of 2x³ +x² -2x-1. Also factorise completely

$\large\sf{To \: \: \: Prove:-}$

(x+1) is a factor of 2x³ +x² -2x-1.

$\large\sf{Theorem:-}$

Apply Factor Theorem

$\large\sf{Solution}$

x+1=0

So x= -1

2x³+x²-2x-1

Replace x by -1, we get

2(-1)³ + (-1)² -2(-1) -1 = -2 +1 +2 -1 = 0

$\huge\sf{Proof}$

Reminder is 0 so that x + 1 is a factor of 2x³ +x² -2x-1.

$\huge\sf\red{Proved}$

hope it helps you!!