Question

What is the factored form of y^2+6y-16

Answer 1

Answer:

y=2 y=-8

Step-by-step explanation:

y^2+6y-16=0

this is a quadratic equation

we are going to factor as you have mention you want it solved with factorization;

The first term is,  y2  its coefficient is  1 .

The middle term is,  +6y  its coefficient is  6 .

The last term, "the constant", is  -16  

Multiply the coefficient of the first term by the constant   1 • -16 = -16

Find two factors of  -16  whose sum equals the coefficient of the middle term, which is   6 .

-2+8 = 6

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  8  

                    y^2 - 2y + 8y - 16

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

                   y • (y-2)

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

                   8 • (y-2)

Add up the four terms

(y+8)  •  (y-2)

 Which is the desired factorization

y=2 y=-8

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Answer 2

y 2 + 6 y − 16 = ( y + 8 ) ( y − 2 )  

Explanation:

Note that in general:

( y + a ) (y − b ) = y 2 + ( a − b ) y − a b

So we want to find a pair of factors  a  and  b  of  16  which differ by  6 .  

The pair  8 , 2 works in that  8− 2 = 6  and  8 ⋅ 2= 16 .

Hence:

y 2 + 6 y − 16 = ( y+ 8 ) ( y − 2 )

y=2,-8