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# Find the quotient and remainder on dividing p(x)=x3−6x2+15x−8 by g(x)=x−2

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## p(x)=x3−6x2+15x−8∴ degree of p(x) is 3.g(x)=x−2∴ degree of g(x) is 1.∴ degree of quotient q(x)=3−1=2, and degree of remainder r(x) is zero.Let, q(x)=ax2+bx+c (Polynomial of degree 2) and r(x)=k (constant polynomial)By using division algorithm, we havep(x)=[g(x)×q(x)+r(x)]=x3−6x2+15x−8=(x−2)(ax2+bx+c)+k=ax3+bx2+cx−2ax2−2bx−2c+k∴x3−6x2+15x−8=ax3+(b−2a)x2+(c−2b)x−2c+kWe have cubic polynomials on both the sides of the equation.∴ Let us compare the coefficients of x3,x2,x and k to get the values of a,b,c.1=a, it is the coefficient of x3 on both sides−6=b−2a, it is the coefficient of x2 on both sides15=c−2b, it is the coefficient of x on both sides−8=−2c+k, it is the constant term on both sidesLet us solve these equations to get the values of b,c, and k.b−2a=−6∴b=−6+2a∴b=−6+2(1)=−4c−2b=15∴c=15+2b∴c=15+2(−4)=7−2c+k=−8∴k=−8+2c∴k=−8+2(7)=6Hence, q(x)=ax2+bx+c=(1)x2+(−4)x+7=x2−4x+7 and r(x)=k=6∴ the quotient is x2−4x+7 and the remainder is 6.  Suggest Corrections  0      Similar questions  Related Videos   Remainder Theorem
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