5x²-27x+28. do it ...............
Answers
Answer:
STEP
1
:
Equation at the end of step 1
((0 - 5x2) + 27x) - 28
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
-5x2 + 27x - 28 = -1 • (5x2 - 27x + 28)
Trying to factor by splitting the middle term
3.2 Factoring 5x2 - 27x + 28
The first term is, 5x2 its coefficient is 5 .
The middle term is, -27x its coefficient is -27 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 5 • 28 = 140
Step-2 : Find two factors of 140 whose sum equals the coefficient of the middle term, which is -27 .
-140 + -1 = -141
-70 + -2 = -72
-35 + -4 = -39
-28 + -5 = -33
-20 + -7 = -27 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -7
5x2 - 20x - 7x - 28
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (x-4)
Add up the last 2 terms, pulling out common factors :
7 • (x-4)
Step-5 : Add up the four terms of step 4 :
(5x-7) • (x-4)
Which is the desired factorization
Final result :
(4 - x) • (5x - 7)