Aditya determines the remainder of -12x¹⁷+3x⁵-9x²-1/x+1 using the remainder theorem. How does he proceed to the correct answer?

Aditya evaluates the numerator of the expression when x = –1. He finds the remainder of the division to be –1

Step-by-step explanation:

– 12x¹⁷+ 3x⁵ – 9x² – 1 / x + 1

To obtain the answer to question, let us apply the remainder theorem. This is illustrated below:

Assume:

x + 1 = 0

Subtract 1 from both side

x + 1 – 1 = 0 – 1

x = – 1

Next, we shall substitute the value of x into – 12x¹⁷+ 3x⁵ – 9x² – 1. This is illustrated below:

– 12x¹⁷+ 3x⁵ – 9x² – 1

x = – 1

– 12(–1)¹⁷+ 3(–1)⁵ – 9(–1)² – 1

– 12(–1) + 3(–1) – 9(1) – 1

12 – 3 – 9 – 1

= –1

Thus, using the remainder theorem,

– 12x¹⁷+ 3x⁵ – 9x² – 1 / x + 1 will result to –1