Question

Find the remainder when 4x³-3x²+ 4x-2 is divided by X – 1 and X – 2.​

Answer 1

Answer :

3 , 26

Note :

★ Remainder theorem : If a polynomial p(x) is divided by (x - c) , then the remainder obtained is given as R = p(c) .

★ Factor theorem :

If the remainder obtained on dividing a polynomial p(x) by (x - c) is zero , ie. if R = p(c) = 0 , then (x - c) is a factor of the polynomial p(x) .

If (x - c) is a factor of the polynomial p(x) , then the remainder obtained on dividing the polynomial p(x) by (x - c) is zero , ie. R = p(c) = 0 .

Solution :

Let the given polynomial be p(x) .

Thus ,

p(x) = 4x³ - 3x² + 4x - 2

We need to find the remainders , when the given polynomial p(x) is divided by (x - 1) and (x - 2) .

• If x - 1 = 0 , then x = 1 .

Thus ,

The remainder obtained on dividing the given polynomial p(x) by (x - 1) will be given as ;

=> R = p(1)

=> R = 4•1³ - 3•1² + 4•1 - 2

=> R = 4•1 - 3•1 + 4•1 - 2

=> R = 4 - 3 + 4 - 2

=> R = 3

• If x - 2 = 0 , then x = 2 .

Thus ,

The remainder obtained on dividing the given polynomial p(x) by (x - 2) will be given as ;

=> R = 4•2³ - 3•2² + 4•2 - 2

=> R = 4•8 - 3•4 + 4•2 - 2

=> R = 32 - 12 + 8 - 2

=> R = 26

Hence ,

The remainders obtained on dividing the given polynomial by (x - 1) and (x - 2) are 3 and 26 respectively .

Answer 2

Step-by-step explanation:

hope it helps u

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