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The polynomial f(x) leaves a remainder of – 3 and – 7 when divided by (3x – 1) and (x +1) respectively. Find the remainder when f(x) is

Home/Math/The polynomial f(x) leaves a remainder of – 3 and – 7 when divided by (3x – 1) and (x +1) respectively. Find the remainder when f(x) is

The polynomial f(x) leaves a remainder of – 3 and – 7 when divided by (3x – 1) and (x +1) respectively. Find the remainder when f(x) is

Question

The polynomial f(x) leaves a remainder of – 3 and – 7 when divided by (3x – 1) and (x +1) respectively. Find the remainder when f(x) is divided by (3x^2 + 2x -1).

## Answers ( )

Step-by-step explanation:Here, f(x) is the given polynomial.

ByremainderTheorem,When divided by (3x-1),

f(1/3) = -3……..(1)

When divided by (x+1),

f(-1) = -7………(2)

Anotherpolynomialis3x²+2x–1Solving,

3x²+2x-1

= 3x²+3x-x-1

=3x(x+1)-(x+1)

=(3x-1)(x+1)

So

f(x) = (3x-1)(x+1)Qx + (ax+b)

For f(-1),

-7 = -a+b

b= a-7

For f(1/3),

-3 = a/3+b

or, -3 = a/3+a-7

or, 4×3 = 4a

or a = 3

Also, b = 3-7 =-4

Hence, remainder is (3x-4)