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:

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle