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Luv2Teach
The Remainder Theorem tells us to use the x value of the factor and sub it in for x in our polynomial and what we get in the end is the remainder we would get if we did the synthetic division on it or long division.  P(-4)=2(-4)^2+5(-4)-12 is P(-4) = 32 - 20 - 12, and P(-4) = 0.  That means when we divide the polynomial by x + 4, we do not get a remainder and the root x = -4 is a factor of the polynomial. 
MrRoyal

The remainder of dividing 2x² + 5x – 12 by  x + 4 is 0

How to determine the remainder?

The given parameters are:

  • Dividend = 2x² + 5x – 12
  • Divisor =  x + 4

Set the divisor to 0

x + 4 = 0

Solve for x

x = -4

Substitute x = -4 in the dividend to calculate the remainder

Remainder = 2(-4)² + 5(-4) - 12

Evaluate

Remainder = 0

Hence, the remainder of dividing 2x² + 5x – 12 by  x + 4 is 0

Read more about remainder theorem at:

https://brainly.com/question/13328536

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