Question

Show that (a +1) is not a factor of a3 - 2a2 + 3a + 4.​

Answer 1

Answer:

Step-by-step explanation:

ANSWER:-

Let us First assume that (a+1) is a factor.

This is done to verify that will be explained.

So ,

$\boxed{a+1=0}$

$\boxed{\texttt{a = -1}}$

Now placing it directly on polynomial

$a^3- 2a^2 + 3a + 4$,

If it is a factor then it must  be equal to zero .

$\implies (-1)^2-2(-1)+3(-1)+4$

$\implies 1+2-3+4$

$\implies 4 \neq 0$

Hence , a+1 is not a factor of $a^3- 2a^2 + 3a + 4$.

Hence proved.

Note:-

• Assumption was taken so that we can place it directly as equal to zero.
• If we may have not considered it, then it would have been proved
• But in question we need to prove it
• That is why assumption that " Let (a+1) be the factor of polynomial " was taken.