Question

If f(x) is divided by x – 3 then the remainder is 5, and when it is divided by (x - 4) the
remainder is 'O'. Then the remainder when it is divided by (x - 3)(x - 4) is​

Answer 1

Answer:

9th

Maths

Polynomials

Remainder Theorem

Let P(x) be a polynomial, w...

MATHS

Let P(x) be a polynomial, which when divided by x−3 and x−5 leaves remainders 10 and 6 respectively. If the polynomial is divided by (x−3)(x−5) then the remainder is :

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ANSWER

P(x) when divided by x−3 and x−5 leaves remainder 10 and 6 respectively.

From polynomial-remainder theorem, P(3)=10 and P(5)=6

If the polynomial is divided by (x−3)(x−5) then remainder must be of the form ax+b (degree of remainder is less than that of divisor)

⇒P(x)=Q(x)(x−3)(x−5)+(ax+b), where Q(x) is some polynomial.

Substituting for x=3 and x=5:

P(3)=10=3a+b

P(5)=6=5a+b

Solving for a and b, we get

a=−2 and b=16

⇒Remainder=−2x+16

Answer 2

ans

ans=

remainder therom =

-5x+20