Find the requested value If Px 20x5 25x4 20x2 and qx 5x2

Find the requested value. If P(x) = 20x^5 - 25x^4 + 20x^2 and q(x) = 5x^2 find (p/q) (-1) A. -3 B. -5 C. 13 D. -13

Solution

Given that

p(x) = 20x⁵ - 25x⁴ + 20x²

= 5x²(4x³ - 5x² + 4)

q(x) = 5x²

p(x)/q(x) =  5x²(4x³ - 5x² + 4) / 5x²

= 4x³ - 5x² + 4

Hence ,

( p/q)(x) = 4x³ - 5x² + 4

  ( p/q)(-1) = 4(-1)³ - 5(-1)² + 4

= 4(-1) - 5(1) + 4

= -4 - 5 + 4

= -5

Therefore ,

  ( p/q)(-1) = -5