Question

Use the remainder theorem to find P (1) for P(x) = 2x^ – 2x²+2x–7.Specifically, give the quotient and the remainder for the associated division and the value of P (1).DOcoQuotient = 0X Х5?RemainderP (1) = 0

Answer 1

In order to find P(1) using the remainder theorem, let's divide the polynomial P(x) by (x - 1):

2x^4 divided by x = 2x^3

2x^3 times (x - 1) = 2x^4 - 2x^3

2x^4 – 2x^3 + 2x – 7 minus (2x^4 - 2x^3) = 2x - 7

2x divided by x = 2

2 times (x - 1) = 2x - 2

2x - 7 minus (2x - 2) = -5

So the result is:

quotient = 2x^3 + 2

Remainder = -5

P(1) = -5