Question

On dividing P(x)=3x^3+x^2+2x+5 by a polynomial g(x), the quotient
and remainder obtained are (3x - 5)and (9x + 10) respectively. Find g(x)​

Answer 1

Question :-

• On dividing p(x)=3x^3+x^2+2x+5 by a polynomial g(x), the quotient and remainder obtained are (3x - 5)and (9x + 10) respectively. Find g(x)

Answer

Given :-

• On dividing p(x)=3x³ + x² + 2x + 5 by a polynomial g(x), the quotient q(x) and remainder r(x) obtained are (3x - 5)and (9x + 10) respectively.

To Find :-

• The divisor g(x).

Concept used :-

• Division Algorithm p(x) = g(x) × q(x) + r(x)

Solution :-

Here, p(x)=3x³ + x² + 2x + 5

quotient, q(x) = 3x - 5

remainder, r(x) = 9x + 10

Using, Division Algorithm

p(x) = g(x) × q(x) + r(x)

3x³ + x² + 2x + 5 = g(x) × (3x - 5) + 9x + 10

⇛ g(x) × (3x - 5) = 3x³ + x² + 2x + 5 - 9x - 10

⇛ g(x) × (3x - 5) = 3x³ + x² - 7x - 5

$\bf\implies \:g(x) = \dfrac{3x³ + x² - 7x - 5}{3x - 5}$

On using long division, we get

$\bf\implies \:g(x) = {x}^{2} + 2x + 1$

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