Question

find the remainder if x³-4x2+ 5x + 3 is divided by (x+2)​

Answer 1

Answer:

The Remainder theorem states that, when f(x) is divided by (x−a)

f(x)=g(x)(x−a)+r

Where g(x) is the quotient and r is the remainder.

If for some x we can make g(x)(x−a)=0, then we have:

f(a)=r

From example:

x3−4x2+12=g(x)(x+2)+r

Let x=−2

∴

(−2)3−4(−2)2+12=g(x)((−2)+2)+r

−12=0+r

r=−12

This theorem is just based on what we know about numerical division. i.e.

The divisor x the quotient + the remainder = the dividend

∴

64=1 + remainder 2.

4×1+2=6

!! May This help You !!

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