Question

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

Answer 1

Answer:

Let g(x) = y

now

divisor * quotient + remainder  = dividend

y * (3x+10) + 16x-43 = 3x^3 + 4x² + 5x - 13

y * (3x+10) = 3x^3 + 4x² - 11x + 30

now we can calculate the value of y by dividing

3x^3 + 4x² - 11x +30 from  3x+10

so 

y = x² - 2x + 3

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Answer 2

Answer:

Step-by-step explanation:

et g(x) = y

now

divisor * quotient + remainder  = dividend

y * (3x+10) + 16x-43 = 3x^3 + 4x² + 5x - 13

y * (3x+10) = 3x^3 + 4x² - 11x + 30

now we can calculate the value of y by dividing

3x^3 + 4x² - 11x +30 from  3x+10

so  

y = x² - 2x + 3