Question

find the remainder when the polynomial p( x) =2 x3 -5x3+3x+7is divided (3x+6)? answer​

Answer 1

Answer:-

Given:-

p(x) = 2x³ - 5x³ + 3x + 7 [Dividend]

Let,

g(x) = 3x + 6 [Divisor]

Zero of g(x) :-

3x + 6 = 0

→ 3x = - 6

→ x = - 6/3

→ x = - 2

Now, putting the value of the zero of g(x) to p(x) :-

∵ p(x) = 2x³ - 5x³ + 3x + 7

= - 3x³ + 3x + 7

∴ p(- 2) = - 3(- 2)³ + 3(- 2) + 7

= 3(8) - 6 + 7

= 24 - 6 + 7

= 18 + 7

= 25

∴ According to the remainder theorem, the remainder would be ‘25’.

Answer 2

g(x) = 3x + 6 = 0

→ 3x = 0 - 6

→ 3x = -6

→ x = -6 ÷ 3

.°. x = -2

p(x) = 2x³ - 5x³ + 3x + 7

Putting the value of x

→ 2(-2)³ - 5(-2)³ + 3(-2) + 7

→ 2(-8) - 5(-8) + (-6) + 7

→ -16 + 40 - 6 + 7

→ 24 + 1

→ 25

.°. The remainder is 25....