Question

Find the remainder when p(x) = –2x5 + x4 + 5x3 + 4x + 1 is divided by (x - 2).

Answer 1

The remainder when p(x) = -2x⁵+x⁴+5x³+4x+1 is divided by (x-2) is 1.

To solve the question above, we make use of the remainder theorem.

Remainder Theorem: It states that if a function F(x) is divided by (x-a), the remainder is F(a).

From the question,

Given:

• Dividend ⇒ p(x) = -2x⁵+x⁴+5x³+4x+1
• Divisor ⇒ (x-2)

in view of the above and applying the Remainder theorem, The remainder will be p(2)

• p(2) = -2(2⁵)+2⁴+5(2³)+4(2)+1
• p(2) = -64+16+40+8+1
• p(2) = 1

hence the remainder when p(x) = -2x⁵+x⁴+5x³+4x+1 is divided by (x-2) is 1

Learn more about  the remainder theorem here: brainly.com/question/13328536