Question

on dividing 3x cube + x square + 2x + 5 by a polynomial g(x), the quotient and remainder are (3x - 5) and ( 9x + 10 )respectively.Find g(x)

Answer 1

here is your answer
g (x)=x square+two x+1
if it help mark as brainlist
(3x-5)÷3xcube +xsquare-5
=g (x)
g (x)=x square +2x +1

Answer 2

Answer:

g(x) = x² + 2x + 1

Step-by-step explanation:

Let p(x) = 3x³ + x² + 2x + 5  ,  q(x) = 3x - 5  and r(x) = 9x + 10

To find : g(x) such that it divided p(x)

we use the division algorithum,

a = bq + r

where a = dividend  , b = divisor ,  q =  quotient and r = remainder

⇒ p(x) = g(x)× q(x) + r(x)

⇒ 3x³ + x² + 2x + 5 = g(x)× (3x - 5) + (9x + 10)

3x³ + x² + 2x + 5 - (9x + 10) = g(x)× (3x - 5)

3x³ + x² - 7x - 5 = g(x)× (3x - 5)

$g(x)=\frac{3x^3+x^2-7x-5}{3x-5}$

Long Division is attached.

g(x) is quotient of the division.

Therefore, g(x) = x² + 2x + 1