Question

factorise using middle term splitting
(a) -y^2+2y+63 ​

Answer 1

The first term is, y2 its coefficient is 1 .
The middle term is, -2y its coefficient is -2 .
The last term, "the constant", is -63

Step-1 : Multiply the coefficient of the first term by the constant 1 • -63 = -63

Step-2 : Find two factors of -63 whose sum equals the coefficient of the middle term, which is -2 .

-63 + 1 = -62
-21 + 3 = -18
-9 + 7 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 7
y2 - 9y + 7y - 63

Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-9)
Add up the last 2 terms, pulling out common factors :
7 • (y-9)
Step-5 : Add up the four terms of step 4 :
(y+7) • (y-9)
Which is the desired factorization

Equation at the end of step
1
:

(y + 7) • (y - 9) = 0