Question

On dividing 3x cube + x square + 2x + 5 by a polynomial G(x), the quotient and remainder are (3x-5) and (9x + 10) respectively. Find G(x)
If anyone first gives ans of this ques. then I will make him brainlist if it is correct....

Answer 1

Refer attachment

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Answer 2

Answer:

The polynomial g(x) is $x^2+2x+1$.

Step-by-step explanation:

The given polynomial is

$f(x)=3x^3+x^2+2x+5$

If the polynomial f(x) divided by a polynomial G(x), then quotient and remainder are (3x-5) and (9x + 10) respectively.

$\frac{3x^3+x^2+2x+5}{g(x)}=3x-5+\frac{9x+10}{g(x)}$

Multiply both sides by g(x).

$3x^3+x^2+2x+5=g(x)(3x-5)+9x+10$

$3x^3+x^2+2x+5-(9x+10)=g(x)(3x-5)$

$g(x)=\frac{3x^3+x^2-7x-5}{3x-5}$

Using long division method we get

$g(x)=x^2+2x+1$

Therefore the polynomial g(x) is $x^2+2x+1$.