∴ degree of p(x) is 3.
∴ 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 have
We 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 sides
15=c−2b, it is the coefficient of x on both sides
−8=−2c+k, it is the constant term on both sides
Let us solve these equations to get the values of b,c, and k.
∴ the quotient is x2−4x+7 and the remainder is 6.