Question

Simplify (x − 3)(x2 + 7x − 8).

Answer 1

So:

1.1 Factoring x2+7x-8

The first term is, x2 its coefficient is 1 .
The middle term is, +7x its coefficient is 7 .
The last term, "the constant", is -8

Step-1 : Multiply the coefficient of the first term by the constant 1 • -8 = -8

Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is 7 .

-8 + 1 = -7
-4 + 2 = -2
-2 + 4 = 2
-1 + 8 = 7 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 8
x2 - 1x + 8x - 8

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-1)
Add up the last 2 terms, pulling out common factors :
8 • (x-1)
Step-5 : Add up the four terms of step 4 :
(x+8) • (x-1)
Which is the desired factorization

Final result :

(x - 3) • (x + 8) • (x - 1)

Does this help?