Question

10. On dividing 3x + x2 + 2x +5 by a polynomial g(x), the quotient and
remainder are (3x - 5) and (9x + 10) respectively. Find g(x).
(3x + x2 + 2x + 5) - (9x + 10)
(3x-5).
HINT​

Answer 1

Answer:

divisor g(x) = x² + 2x + 1

Step-by-step explanation:

divident= 3x³ + x² + 2x + 5

divisor = ?

quotient = 3x - 5

reminder = 9x + 10

divident = divisor × quotient + reminder

x²+3x³+2x+5 = g(x) × (3x-5) + (9x+10)

x²+3x³+2x+5 - (9x+10) = g(x) × (3x-5)

x²+3x³+2x+5-9x-10 = g(x) × (3x-5)

x² + 3x3 -7x - 5 = g(x) × (3x - 5)

(x² +3x³ - 7x -5)/(3x - 5) = g (x)

3x-5 ¦................................¦ x² + 2x + 1

¦ 3x³ + x² - 7x - 5 ¦

3x³ - 5x²

- +

6x² - 7x - 5

6x² - 10x

- +

3x - 5

3x - 5

- +

0

g (x) = x² + 2x + 1