Find the remainder when the polynomial 2x^4+x^3-+4x^3-3x-2 is divided by x-3 without using long division
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Answer:
HEY BUDDY
What is the remainder when 2x^4-6x^3+2x^2-x+2/x+2?
Why do toppers choose BYJU'S for JEE preparation?
Soln: 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.