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 .

(2,6)

step-by-step explanation:

cause i just did this and got the answer

you're welcome

all three statements are true

step-by-step explanation:

a shipping fee of 5% is charged online with every item purchased online

first let's just take each option and calculate them based on this, to see if the answers matched

keith buys a 40 dollar book

40 x 0.05 = 2

therefore there will be a two dollar fee on keith's book

40 + 2 =42

the first statement is true

a chair costs $80

80 x 0.05 = 4

80 + 4 = 84

the second statement is true

george buys a 20 dollar calculator

20 x 0.05 = 1

20 + 1 = 21

the third statements are true

all three statements are true