Question

On dividing 3x^3+4x^2+5x-13 by a polynomial g(x) the quotient and the remainder were 3x+10 and 16x-43 respectively. Find g(x)

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

♤♤RULE♤♤

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

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

♤♤SOLUTION♤♤

Here, we consider :

f(x) = 3x³ + 4x² + 5x - 13

q(x) = 3x + 10

r(x) = 16x - 43

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

(3x³ + 4x² + 5x - 13) = (3x + 10).g(x) + (16x - 43)

=> (3x + 10).g(x) = (3x³ + 4x² + 5x - 13) - (16x - 43)

=> (3x + 10).g(x) = 3x³ + 4x² + 5x - 13 - 16x + 43

=> (3x + 10).g(x) = 3x³ + 4x² - 11x + 30

=> (3x + 10).g(x) = (3x+10)(x² - 2x + 3)

Cancelling (3x + 10), we get :

g(x) = (x² - 2x + 3)

♤♤TRICK♤♤

3x³ + 4x² - 11x + 30

= 3x³ + 10x² - 6x² - 20x + 9x + 30

= x²(3x + 10) - 2x(3x + 10) + 3(3x + 10)

= (3x+10)(x² - 2x + 3)

♧♧HOPE THIS HELPS YOU♧♧

Answer 2

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