Question

the polynomials kx*3+3x*2-8 and 3x*3-5x+k are divided by x+2. if the remainder in each case is the same then find k.

Answer 1

Hlo friend.. Cutiepie Here..

Here is ur answer :

Let P( x) = kx³ + 3x² - 8 and

H( x) = 3x³ - 5x + k

When we divide p(x) by x + 2, then we get the remainder p(-2)

Now,

P(-2) = k(-2)³ + 3(-2)² - 8

= - 8k + 3 × 4 - 8

= - 8k + 12 - 8

= - 8k + 4.

When we divide h(x) by x + 2, then we get the remainder h(-2)

H(-2) = 3(-2)³ - 5(-2) + k

= 3 × - 8 + 10 + k

= - 24 + 10 + k

= - 14 + k

According to question, both the remainders are equal.

I. E. ,

P(-2) = H(-2)

-8k + 4 = - 14 + k

-8k - K = - 14 - 4

-9k = - 18

( Both sides minus cancel out)

9k = 18

k = 18 / 2

k = 2

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HOPE IT HELPS YOU..