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 .

use substitution to solve each system of equations. y = x + 5 3x + y = 25 62/87,21 y = x + 5 3x + y = 25 substitute x + 5 for y in the second equation. substitute the solution for x into either equation to find y. the solution is (5, 10)

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step-by-step explanation:

$15 each

step-by-step explanation:

$45/3 children= $15 each