Question

On dividing the polynomial 3x3+4x2+5x-13 by the polynomial g(x) , the quotient and the remainder were (3x+10) and (16x-43) respectively. Find g(x)

Answer 1

q=3x+10
r=16x-43
d=3x³+4x²+5x-13
g=????
so from above solution the answer is
g(x)= x²-2x+3

Answer 2

Answer:

Dividend = $3x^3+4x^2+5x-13$

Quotient = 3x+10

Remainder = 16x-43

To find divisor

$Dividend = (Divisor \times Quotient)+Remainder$

$3x^3+4x^2+5x-13 = (Divisor \times (3x+10))+(16x-43)$

$3x^3+4x^2+5x-13 - (16x-43)= (Divisor \times (3x+10))$

$3x*3+4x^2-11x+30= (Divisor \times (3x+10))$

$\frac{3x*3+4x^2-11x+30}{3x+10}= Divisor$

$\frac{3x*3+4x^2-11x+30}{3x+10}= Divisor$