Question

Solve by factoring y²-4=3y

Answer 1

y =-1

y=4

Explanation:

`y^2-4=3y\\\mathrm{Subtract\:}3y\mathrm{\:from\:both\:sides}\\y^2-4-3y=3y-3y\\\\\mathrm{Simplify}\\y^2-3y-4=0\\\\\mathrm{Solve\:by\:factoring}\\\mathrm{Factor\:}y^2-3y-4:\quad \left(y+1\right)\left(y-4\right)\\\\\mathrm{Solve\:}\:y+1=0:\quad y=-1\\\mathrm{Solve\:}\:y-4=0:\quad y=4\\\\y=-1,\:y=4`

Answer 2

(y + 1) • (y - 4)

Explanation:

Trying to factor by splitting the middle term

1.1 Factoring y2-3y-4

The first term is, y2 its coefficient is 1 .

The middle term is, -3y its coefficient is -3 .

The last term, "the constant", is -4

Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4

Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3 .

-4 + 1 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 1

y2 - 4y + 1y - 4

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

y • (y-4)

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

1 • (y-4)

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

(y+1) • (y-4)

Which is the desired factorization

Final result :

(y + 1) • (y - 4)