Divide p x by q x ifi p x - 2x3 - 11x2 - 4x - 5- q x - 2x - 1ii p x - x3 - 316x2 - 2x - 4-q x - 1 - 3x2

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Synthetic Division of Polynomials

Divide p x ...

Question

Divide $p (x) by q (x) if$
(i) $p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5, q (x) = 2 x + 1$
(ii) $p (x) = x^{3} + \frac{31}{6} x^{2} - 2 x + 4, q (x) = 1 + \frac{3 x}{2}$

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Now in each of the following, find the quotient and remainder on dividing p(x) by q(x) and write then in the form p(x) = u(x) q(x) + v(x).

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

p (x)

g (x)

q (x)

r (x)

p (x)

p (x) = x^{2} - 2 x + 1

q (x) = x^{3} - 3 x^{2} + 2 x - 1

p (x) \times q (x)

p (x) \times q (x)

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.

(i)

(ii)

(iii)

(iv)

(v)

For each pair of polynomials p(x) and q(x) given below find the degree of p(x) + q(x) and p(x)q(x).

(i)

(ii)

(iii)

(iv)

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