If x2+x-12 divides p(x) = x3+x2+bx-84 exactly. Find a and b

1.	If x2+x-12 divides p(x) = x3+x2+bx-84 exactly. Find a and b
Answer» X2+x-12 =0\xa0x2+ 4x-3x-12=0x(x+4)-3(x+4)=0(x-3) (x+4) =0so x= 3or. x=-4p(x)÷g(x)= q(x) + rp(x)÷g(x)= q(x) +0x3 + ax2 + bx -84 ÷ x2+x-12after dividing remainder will be ax2 - x2+bx+12x-84=0let x=327a-9+3b+36-84=09a + 3b= 573(3a+b)=573a+b=19________eq 1now let x= -4ax2-x2+bx+12x-84=016a-16-4b-48-84=016a-4b=1484(4a-b)=1484a-b=37_________eq 2add equation 1 and equation 2so ,3a + b +4a -b = 19+377a = 56a= 8put a=8 in equation 13a+b = 1924 +b=19or b=-5

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