Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

ANSWER

The completely factored form is

EXPLANATION

The given polynomial expression is

Let

According to the Remainder Theorem, if f(x) is exactly divisible by x-1, then the remainder is zero.

This implies that:

When we substitute the value of p back into the function, f(x) we get:

We now perform long division as shown in the attachment.

We can factor the function to get:

We now split the middle term of the quadratic term and factor it completely to obtain:

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