Question

find the remainder when f(x)=9x^3-3x^2+14x-3 is divided by g(x)=3x-1

Answer 1

g(x)= 3x-1
0= 3x-1
1= 3x
1/3 = x


f(x)= 9x^3-3x^2+14x-3
= 9×1/3^3-3×1/3^2+14x-3
=+1/3-1/3+14/3-3
= 14/3-3/1
=(14-9)/3
= 5/3

Answer 2

Concept

According to the remainder theorem, the polynomial f(x) is divided by (x - h), and the result is f. (h).

Given

Given that

•  f(x)=9x^3-3x^2+14x-3  
•  g(x) = 3x - 1 = 0

Find

We need to find the remainder

Solution

Now ,

g(x) = 3x - 1 = 0

∴ 3x = 1

∴ x = (1/3)

Therefore ,

f(x) = 9x^3-3x^2+14x-3

∴ f(1/3) = 9(1/3)³ - 3(1/3)² + 14(1/3) - 3

∴ f(1/3) = 9(1/27) - 3(1/9) + (14/3) - 3

∴ f(1/3) = (1/3) - (1/3) + (14 - 9)/3

∴ f(1/3) = (5/3)

Hence the remainder is 5/3

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