10. Complete.

y^2 + 15y + 56 = (y + 7)(y + )

A. 8

B. –7

C. –8

D. 7

I would go with letter B. -7

Step-by-step explanation:

The two factors of a quadratic equation can be multiplied to form the original equation. Let the missing term be a:

y² + 15y + 56 = (y + 7)(y + a)

y² + 15y + 56 = y² + (7 + a)y + 7a

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Step by Step Solution

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Step by step solution :

STEP  1 :

Trying to factor by splitting the middle term

1.1     Factoring  y2+14y+49  

The first term is,  y2  its coefficient is  1 .

The middle term is,  +14y  its coefficient is  14 .

The last term, "the constant", is  +49  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 49 = 49  

Step-2 : Find two factors of  49  whose sum equals the coefficient of the middle term, which is   14 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  7  and  7  

                    y2 + 7y + 7y + 49

Step-4 : Add up the first 2 terms, pulling out like factors :

                   y • (y+7)

             Add up the last 2 terms, pulling out common factors :

                   7 • (y+7)

Step-5 : Add up the four terms of step 4 :

                   (y+7)  •  (y+7)

The solution is:

  y  =  -7  

 The solution is:

 y = -14 / 2 = -7

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