Question

When (5x³ + ax + b) is divided by ( (x-2) ), the remainder is equal to the remainder obtained when the same expression is divided by ( (x+2) ).

A) Explain why.

B) Find the value of A.

Answer 1

To find the remainder when (5x³ + ax + b) is divided by (x-2) and (x+2), use the Remainder theorem. The value of A is -20.

Step-by-step explanation:

To find the remainder when (5x³ + ax + b) is divided by (x-2) and (x+2), we can use the Remainder theorem. According to the Remainder theorem, if a polynomial f(x) is divided by (x - c), then the remainder is equal to f(c).

Let's find the remainders when (5x³ + ax + b) is divided by (x - 2) and (x + 2). When divided by (x - 2), the remainder is equal to f(2), and when divided by (x + 2), the remainder is equal to f(-2).

So, f(2) = 5(2)³ + a(2) + b and f(-2) = 5(-2)³ + a(-2) + b. Since both these remainders are equal, we have:

5(2)³ + 2a + b = 5(-2)³ - 2a + b.

By simplifying this equation, we get:

40 + 2a + b = -40 - 2a + b.

By comparing the like terms, we find that 4a must be equal to -80.

To find the value of A, we divide both sides of the equation by 4: A = -80/4 = -20.