Question

plz plz correct information ...help me plz... guys....​

Answer 1

Answer:

$g(x) = x^2+2x+3$

Step-by-step explanation:

We know that

Dividend = Divisor × Quotient + Remainder

Let Dividend = p (x), Divisor = g (x), Quotient = q (x) and Remainder = r (x).

$\therefore p(x) = g(x) \times q(x) + r(x)$

Given $p(x) = 3x^3 + x^2 + 2x + 6, q(x) = 3x - 5 \text{ and } r(x) = 3x + 21$

$g(x) = ?$

$\therefore 3x^3 + x^2 + 2x + 6 = g(x) \times (3x - 5) + 3x + 21$

$\Rightarrow 3x^3 + x^2 + 2x + 6 - 3x - 21 = g(x) \times (3x - 5)$

$\Rightarrow 3x^3 + x^2 - x - 15 = g(x) \times (3x - 5)$

$\Rightarrow \cfrac{3x^3 + x^2 -x - 15}{3x - 15} = g(x)$

$\therefore g(x) = x^2+2x+3$

Please mark my answer as BRAINLIEST.