Question

Find the remainder, when (without division) 4x -3x2+2x-4 is
divisible by (x+2)​

Answer 1

We have various methods to solve this problem like common division, remainder theorem, factor theorem, synthetic division. But, very easy method in these are synthetic division, remainder theorem and factor theorem that according to me. So, now I'll explain in the reminder theorem.

So, let x+2=0.

=> x = 0–2

x = -2

Therefore, we get the value of 'x', that is -2. So, now substitute the -2 in the given equation.

f(x) = 2x⁴-6x³+2x²-x+2

=> f(-2) = 2(-2)⁴-6(-2)³+2(-2)²-(-2)+2

f(-2) = 2(16)-6(-8)+2(4)+2+2

f(-2) = 32+48+8+2+2

f(-2) = 92

Therefore, 92 will be the remainder for the given equation. So, 92 is the answer for your problem. Thank You.

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