x^2+38x+961 middle term split
Answers
Answer:
Step-by-step explanation:
Step by step solution :
STEP
1
:
Equation at the end of step 1
(31x2 - 38x) + 7 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 31x2-38x+7
The first term is, 31x2 its coefficient is 31 .
The middle term is, -38x its coefficient is -38 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 31 • 7 = 217
Step-2 : Find two factors of 217 whose sum equals the coefficient of the middle term, which is -38 .
-217 + -1 = -218
-31 + -7 = -38 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -31 and -7
31x2 - 31x - 7x - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
31x • (x-1)
Add up the last 2 terms, pulling out common factors :
7 • (x-1)
Step-5 : Add up the four terms of step 4 :
(31x-7) • (x-1)
Which is the desired factorization