Paragraph: Let f(x), g(x) and h(x) be function of degree more than 5 and (x) (x)= | array ccc x f(x)+f^ ( ) & x g(x)+g^ ( ) & x h(x)+h^ ( ) -2 f( )+3 f^ ( ) & -2 g( )+3 g^ ( ) & -2 h( )+3 h^ ( ) f^ ( ) & g^ ( ) & h^ ( ) array | Question: Le

Question

Paragraph: Let f(x), g(x) and h(x) be function of degree more than 5 and (x) (x)= | array ccc x f(x)+f^ ( ) & x g(x)+g^ ( ) & x h(x)+h^ ( ) -2 f( )+3 f^ ( ) & -2 g( )+3 g^ ( ) & -2 h( )+3 h^ ( ) f^ ( ) & g^ ( ) & h^ ( ) array | Question: Let =1 and f(x)=x^5+2 x^4, g(x)=x^7-x^8, h(x)=1+x-x^9 then remainder when. (x) is divided by x^2-1

Quantrex Academy · Accepted Answer

Correct answer: B. 176(x-1)

By applying R₁ R₁-R₃, R₂ R₂-3 R₃ (x)=-2 x | array lll f(x) & g(x) & h(x) f( ) & g( ) & h( ) f^ ( ) & g^ ( ) & h^ ( ) array | Clearly ( )=0, ^ ( )=0 As ( x ) is divided by x ^2-1 remainder will be ax +b (linear) aligned & (x)= (x^2-1 ) Q(x)+a x+b & (1)=a+b=0 & (-1)=-a+b=-352 & a x+b=176(x-1) aligned

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