Question

To find the answer,the remainder theorem must be used,,specifically give the quotient and the remainder for the associated division and the value of P(3).

Answer 1

The quotient is 2x² + x + 3

The reminder is 2

P(3) = 2

How to divide polynomial.

Let's perform the long division for 2x³ - 5x² - 7 divided by x - 3.

2x² + x + 3

______________________

x - 3 | 2x³ - 5x² - 7

- (2x³ - 6x²)

____________

x² - 7

- (x² - 3x)

__________

3x - 7

- (3x - 9)

__________

2

So, the quotient is 2x² + x + 3 and the remainder is 2.

P(x) = 2x³ - 5x² - 7

P(3) = 2(3)³ - 5(3)² -7

= 2(27) - 5(9) -7

= 54 - 45 -7

= 2

Therefore, P(3) = 2