Question

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Two polynomial f(x)=3x³ - 5x² - 10 and g(x)= x³ + 5x - 3 . when both divided by (x - 2) the remainder are r1 and r2 . find the value f (r1 + r2 - r1×r2) .

Answer 1

Answer:

The polynomials ax3−3x2+4 & 2x3−5x+a when (x−2) leaves remainders p and q & if p−2q=4 find a.

A .

a=2

B .

a=4

C .

a=6

D .

both a and b

It is given that a polynomial ax3−3x2+4 when divided by (x−2) leaves the remainder p. Let us substitute x=2 in ax3−3x2+4 and equate it to p as follows:

a(2)3−3(2)2+4=p⇒(a×8)−(3×4)+4=p⇒8a−12+4=p⇒8a−8=p....(1)

Similarly, given a polynomial 2x3−5x+a when divided by (x−2) leaves the remainder q. Let us substitute x=2 in 2x3−5x+a and equate it to q as follows:

2(2)3−(5×2)+a=q⇒(2×8)−10+a=q⇒16−10+a=q⇒6+a=q....(2)

It is also given that p−2q=4, we, now substitute the values of p and q from equations 1 and 2 as shown below:

p−2q=4⇒8a−8−