Question

can x minus 7 be the remainder on dividing of a polynomial p x by 7 x + to justify your answer​

Answer 1

Division Algorithm for Polynomials states that, " If p(x) and d(x) are polynomials such that d(x) ≠ 0, then there exists polynomials, q(x) and r(x) such that,  p(x) = d(x).q(x) + r(x),    where, deg(r(x)) < deg(d(x)) or r(x) = 0. " Here, q(x) is called the quotient and r(x) is remainder. Now, Given: r(x) = (x + 1) ⇒ deg(r(x)) = 1 d(x) = (2x - 5)⇒ deg(d(x)) = 1 = deg(r(x)) Thus, according to Division algorithm of Polynomials, it is not possible.