On dividing - by a polynomial - the quotient and remainder were - and - respectively- Find the polynomial -

Step 1: Write the terms in the standard form 3𝒙^𝟑+4𝒙^𝟐+5𝒙−𝟏3 = (3x+10)g(x) + (16x 43) and then simplify for g(x) nbsp; nbsp; g(x)=3𝒙^𝟑+4𝒙^𝟐 𝟏1𝒙+30/3x+10 ...

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Byju's Answer

Standard VI

Mathematics

Formation of Algebraic Expressions

On dividing �...

Question

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

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Solution

Step 1: Write the terms in the standard form

$3 x^{3} + 4 x^{2} + 5 x - 13 = (3 x + 10) g (x) + (16 x - 43)$ and then simplify for g(x)
$g (x) = \frac{3 x^{3} + 4 x^{2} - 11 x + 30}{3 x + 10}$

Step 2: Perform the division algorithm to find g(x)

divide the polynomial $3 x^{3} + 4 x^{2} - 11 x + 30$ by $3 x + 10$ using the long division method.
The quotient is $x^{2} - 2 x + 3$ and remainder $0$

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On dividing 3x3+4x2+5x−13 by a polynomial 𝒈(𝒙), the quotient and remainder were 3x+10 and 16x−43 respectively. Find the polynomial 𝒈(𝒙).

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