Question

Use factor theorem to show that x4+2x3−2x2+2x−3 is exactly divisible by x−3.

Answer 1

Answer:

Step-by-step explanation:

Let p(x)=x4+2x3−2x2+2x−3andg(x)=x+3. Then , g(x)=0⇒x+3=0⇒x=−3.

By factor theorem , p (x) will be exactly divisible by x+3 , if p(−3)=0.

Now , p(−3)={(−3)4+2×(−3)3−2×(−3)2+2×(−3)−3}

=(81−54−18−6−3)=0.

Since p(−3)=0 , it follows that p (x) is exactly divisible by (x+3).