What is the remainder when (3x4 + 2x3 − x2 + 2x − 19) ÷ (x + 2)?

The remainder will be 5 only.

Explanation:

Since we have given that

and

Now, using the division algorithm, we'll get,

When we compare it with  division lemma, which says that

We get,

Hence, the remainder will be 5 only.

Remainder=5

Step-by-step explanation:

We know that the Remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial (x-a) is equal to f(a).

Here

The linear polynomial =

Hence, the remainder of the given division problem is 5.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5