If the polynomials ax^3 + 4x^2 + 3x - 5 and x^3 - 3x^2 - 5x + a leave the same remainder when divided by (x-3) and (x+2) respectively, find the value of a

Given:

The polynomials and leave the same remainder when divided by (x-3) and (x+2) respectively.

To find:

The value of a.

Solution:

Remainder theorem: If a polynomial p(x) is divided by (x-c), then the remainder is equal to p(c).

The polynomials is divided by (x-3). So, the remainder is f(3).

The polynomial is divided by (x+2). So, the remainder is g(-2).

It is given that the remainders are same. So,

Divide both sides by 26.

Therefore, the value of a is .

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!