Question

f(x)=9x^3−3x^2+x−5 g(x)=3x−2 find the remainder using remainder theorem..

Answer 1

Step-by-step explanation:

Given:-

f(x)=9x^3−3x^2+x−5

g(x)=3x−2

To find:-

find the remainder using remainder theorem ?

Solution:-

Given polynomials are:

f(x)=9x^3−3x^2+x−5

g(x)=3x−2

We know that

Remainder Theorem:-

Let P(x) be any Polynomial of the degree greater than or equal to 1 and (x-a) is a linear polynomial,if P(x) is divided by (x-a) then the remainder is P(a).

Now g(x) = 3x-2

=>3x-2=0

=>3x = 2

=>x =2/3

If P(x) is divided by g(x) then the remainder is P(2/3).

Put x =2/3 in P(x) then

P(2/3) =>

9(2/3)^3 - 3(2/3)^2 +(2/3) -5

=>9(8/27) - 3(4/9) +(2/3) -5

=> [(9×8)/27 ] - [(3×4)/9] +(2/3) -5

=>(72/27) -(12/9) +(2/3) -5

=>(8/3) -(4/3) +(2/3) -5

LCM = 3

=>[(8×1)-(4×1)+(2×1)-(5×3)]/3

=> (8-4+2-15)/3

=> (10-19)/3

=>-9/3

=> -3

Remainder = -3

Answer:-

Remainder for the given problem is -3

Used formula:-

Remainder Theorem:-

Let P(x) be any Polynomial of the degree greater than or equal to 1 and (x-a) is a linear polynomial,if P(x) is divided by (x-a) then the remainder is P(a).