Math, asked by neerajsingh57362, 1 day ago

(y ²+ 7y + 10) ÷ (y + 5)

Answers

Answered by niveshkarthikkv
0

Answer:

(y2 + 7y + 10) ÷ (y + 5)

Let us facterise the (y2 + 7y + 10)

By splitting the middle term we need to find the two numbers such that, there

Sum = 7

Product = 10

Let us consider the two numbers 2 and five, so

Sum = 2 + 5 = 7

Product = 2 × 5 = 10

So, we can write

y2 + 7y + 10 = y2 + 2y + 5y + 10

y2 + 2y + 5y + 10 = y (y + 2) + 5(y + 2)

y (y + 2) + 5(y + 2) = (y + 2)(y + 5)

y2 + 7y + 10 = (y + 2)(y + 5)

⇒  

(

y

2

+

7

y

+

10

)

(

y

+

5

)

(y2+7y+10)(y+5)

⇒  

(

y

+

2

)

(

y

+

5

)

(

y

+

5

)

(y+2)(y+5)(y+5)

⇒  

(

y

+

2

)

×

(

y

+

5

)

(

y

+

5

)

(y+2)×(y+5)(y+5)

⇒ (y + 2)

(y2 + 7y + 10) ÷ (y + 5) = (y + 2)

Step-by-step explanation:

Answered by divyapakhare468
1

To solve : ( y^{2} + 7y + 10 )\  \div \ (y + 5 )

Solution :

  • To divide the given algebraic equations we first factorize numerator ( y^{2} + 7y + 10 )  by splitting the middle term.
  • factors of  (y^{2} + 7y + 10 )

                          \begin{array}{l}=y^{2}+2 y+5 y+10 \\=\left(y^{2}+2 y\right)+(5 y+10) \\=y(y+2)+5(y+2)\end{array}  

  • Taking ( y + 2 ) common  

                         =(y+2)(y+5)

  • Now , dividing given equation by substituting above factors of numerator  we get,

                 \begin{array}{l}\left(y^{2}+7 y+10\right) \div(y+5) \\\quad=\frac{y^{2}+7 y+10}{(y+5)} \\\quad=\frac{(y+2)(y+5)}{(y+5)} \\\quad=(y+2) \times \frac{(y+5)}{(y+5)}\end{array}

                     = ( y + 2)

     Hence ,  ( y + 2 )  is the correct answer.

               

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