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Addition and Subtraction of Algebraic Expression

Find the sum ...

Question

Find the sum of the following:
(a) $P (x) = x^{2} - 2 x + 1$ and $Q (x) = x^{3} + 3 x^{2} + 2 x - 1$
(b) $P (t) = 4 t^{3} - 3 t^{2} + 2$ , $Q (t) = t^{4} - 2 t^{3} + 6$ and $R (t) = t^{3} + 4 t^{2} + 4$

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Solution

We need to find sum of the given expressions.
(a) Given, $P (x) = x^{2} - 2 x + 1$ and $Q (x) = x^{3} + 3 x^{2} + 2 x - 1$

Their sum $= P (x) + Q (x) = x^{2} - 2 x + 1 + x^{3} + 3 x^{2} + 2 x - 1$ $= x^{3} + 4 x^{2}$

(b) Given, $P (t) = 4 t^{3} - 3 t^{2} + 2, Q (t) = t^{4} - 2 t^{3} + 6, R (t) = t^{3} + 4 t^{2} + 4$

Their sum $= P (t) + Q (t) + R (t) = 4 t^{3} - 3 x^{2} + 2 + t^{4} - 2 t^{2} + 6 + t^{3} + 4 t^{2} + 4 = t^{4} + 3 t^{3} + t^{2} + 12$

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Similar questions

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)

p (x) by q (x) if

p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5, q (x) = 2 x + 1

p (x) = x^{3} + \frac{31}{6} x^{2} - 2 x + 4, q (x) = 1 + \frac{3 x}{2}

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^{4} - 1

r (x) = x^{3} - 2 x^{2} - 5 x + 6

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