Question

are there any factors for x2-4x+5
prove that .

Answer 1

Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-4x-5

The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 1 • -5 = -5

Step-2 : Find two factors of -5 whose sum equals the coefficient of the middle term, which is -4 .

-5 + 1 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 1
x2 - 5x + 1x - 5

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

Equation at the end of step 1 :
(x + 1) • (x - 5) = 0