Question

The value of
3x³+9x²+24÷3x
is???​

Answer 1

The value of (3x3 +9x2 + 27x) ÷ 3x

= (3x3 + 9x2 + 27x)/3x

Takeout 3x as common,

= 3x (x2 + 3x + 9)/3x = x2 + 3x +

Answer 2

Correct Question :

p(x) = ( 3x³ + 9x² + 27x ) ÷ 3x

Solution :

By using long division method.

Step of long division method :-

★ Divide, multiply, subtract, bring down and repeat or find the remainder.

Calculation is in the attachment.

Now, in order to check the answer.

Let's do verification :

According to the Euclid's division lemma

Dividend = Quotient × Divisor + Remainder

$\implies$p(x) = q(x) × g(x) + r(x)

Where,

" p(x) " = Dividend

" q(x) " = Quotient

" g(x) " = Divisor

" r(x) " = Remainder

Now, as per the question :-

$\implies\bf{q(x) = (x^{2} + 3x + 9)}$

$:\implies\bf{r(x) = 0}$

$:\implies\bf{g(x) = 3x}$

Substitute the respective values in the above division rule :

p(x) = q(x) × g(x) + r(x)

$:\implies\sf{p(x) = (x^{2} + 3x + 9) \times (3x) + 0}$

$\implies\bf{p(x) = ( 3x^{3} + 9x^{2} + 27x)}$

And now, let's compare the value with the p (x)

p(x) = ( 3x³ + 9x² + 27x )

Hence, L. H. S = R. H.S

Verified!!

Therefore,

$\implies$[ x² + 3x + 9 ] is the factor of p (x)

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