Question

on dividing the polynomial 3x³+4x²+5x-13 by g(x).the quotient is 3x+10 and the remainder is 16x-43. find g(x)​

Answer 1

Answer:

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Answer 2

Given that,

let Polynomial p(x)=3x
3
+4x
2
+5x−13

quotient g(x)=3x+10

remainder r(x)=16x−43

g(x)=?

Now,

we know that

Euclid division lemma theorem,

p(x)=g(x)×q(x)+r(x)

3x
3
+4x
2
+5x−13=g(x)×(3x+10)+(16x−43)

3x
3
+4x
2
+5x−13−16x+43=g(x)×(3x+10)

3x
3
+4x
2
−11x+30=g(x)×(3x+10)

g(x)=
3x+10
3x
3
+4x
2
−11x+30
​


now, dividing,

3x+10)3x
3
+4x
2
−11x+30(x
2
−2x+3
−3x
3
+10x
2

_____________
−6x
2
−11x
−6x
2
−20x
_____________
9x+30
9x+30
____________
0
Hence, g(x)=x
2
−2x+3
This is the answer.