Question

On dividing 3x3 - 2x2 + 5x - 5 by a polynomial p(x), the quotient and remainder are x2 - x + 2 and -7 respectively, Find p(x).

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

♤♤RULE♤♤

Let, f(x) be any polynomial. On division by p(x), if it gives quotient q(x) and remainder r(x), the relation is :

f(x) = p(x).q(x) + r(x)

♤♤SOLUTION♤♤

Here, we consider :

f(x) = 3x³ - 2x² + 5x - 5

q(x) = x² - x + 2

r(x) = -7

Now, applying the relation f(x) = p(x).q(x) + r(x), we get :

(3x³ - 2x² + 5x - 5) = (x² - x + 2).p(x) - 7

=> (x² - x + 2).p(x) =(3x³ - 2x² + 5x - 5) + 7

=> (x² - x + 2).p(x) = 3x³ - 2x² + 5x + 2

=> (x² - x + 2).p(x) = (x² - x + 2)(3x + 1)

Now, eliminating (x² - x + 2), we get :

p(x) = 3x + 1

◇◇PLANNING◇◇

3x³ - 2x² + 5x + 2

= 3x³ - 3x² + 6x + x² - x + 2

= 3x(x² - x + 2) + 1(x² - x + 2)

= (3x + 1)(x² - x + 2)

⬆HOPE THIS HELPS YOU⬅

Answer 2

I hope it will help you.....