Step by step solution :

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring a2-8a+15

The first term is, a2 its coefficient is 1 .

The middle term is, -8a its coefficient is -8 .

The last term, "the constant", is +15

Step-1 : Multiply the coefficient of the first term by the constant 1 • 15 = 15

Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is -8 .

-15 + -1 = -16

-5 + -3 = -8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -3

a2 - 5a - 3a - 15

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

a • (a-5)

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

3 • (a-5)

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

(a-3) • (a-5)

Which is the desired factorization

Equation at the end of step

1

:

(a - 3) • (a - 5) =0