Question

Find the remainder when f(x)=12x^3-13^2-5x+7 is divided by 3x+2?

Answer 1

hope it helps you friend

Answer 2

we can find the remainder of the given f(x) by two methods. one is long division method and another one is by remainder theorem.

according to me, remainder theorem is easier.. isn't it??

by remainder theorem :-

given f(x) = 12x³ - 13² - 5x + 7

g(x) = 3x + 2

==> 3x + 2 = 0

==> 3x = -2

==> x = -2/3

on putting values :-

f(-2/3) = 12(-2/3)³ - 169 - 5(-2/3) + 7

= 12(-8/27) - 169 + 10/3 + 7

= 4(-8/9) - 162 + 10/3

= -32/9 - 162 + 10/3

lcm of 9 and 3 = 3 × 3 = 9

= -32/9 - (162×9)/(1×9) + (10×3)/(3×3)

= -32/9 - 1458/9 + 30/9

= -1490/9 + 30/9

= -1460/9

hence, the remainder is -1460/9

HOPE THIS HELPS..!!