Question

Factorise the expressions and divide them as direct

(x +7X+ 10) ÷ (X +5)​

Answer 1

Step-by-step explanation:

We divide the given polynomial 36(x+4)(x

2

+7x+10) by 9(x+4) as shown below:

9(x+4)

36(x+4)(x

2

+7x+10)

=

9

36

×

(x+4)

(x+4)(x

2

+7x+10)

=

3×3

2×2×3×3

×(x

2

+7x+10)

=4(x

2

+7x+10)

Hence,

9(x+4)

36(x+4)(x

2

+7x+10)

=4(x

2

+7x+10).

Answer 2

Correct Question :

Factorise the expressions and divide them as direct :

$\large \bf \: \: \: \: \: \: \red{\bigstar} \frac{(x^2 + 7x +10)}{(x + 5)}$

Answer :

$\large \implies \bf (x + 2)$

Solution :

$\large\large \implies \sf \frac{(x^2 + 7x +10)}{(x + 5)}$

• Split the middle term from numerator.

$\large \large \implies\sf \frac{( x^2 + \underline{5x + 2x} + 10)}{(x + 5)}$

• Make Factors.

$\large \large \implies\sf \frac{(x(x + 5) + 2(x + 5) )}{(x + 5)}$

• Take (x + 5) Common from numerator.

$\large \large \implies\sf \frac{((x + 5) (x + 2) )}{(x + 5)}$

• Cut the like terms from numerator and denominator.

$\large \large \implies\sf \frac{(\cancel{(x + 5)}\: \: (x + 2) )}{\cancel{(x + 5)}}$

$\large \large \implies \boxed{\sf\: \: (x + 2) \: }$

Therefore,

$\large \sf \frac{( x^2 + 7x + 10)}{(x + 5)} = \large (x+2)$

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