Answer:
Step by step solution :
STEP1:Equation at the end of step 1
((49 • (x4)) - (2•7x2)) + 1 = 0
STEP 2 :
Equation at the end of step2:
(72x4 - (2•7x2)) + 1 = 0
STEP3:Trying to factor by splitting the middle term
3.1 Factoring 49x4-14x2+1
The first term is, 49x4 its coefficient is 49 .
The middle term is, -14x2 its coefficient is -14 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 49 • 1 = 49
Step-2 : Find two factors of 49 whose sum equals the coefficient of the middle term, which is -14 .
-49 + -1 = -50 -7 + -7 = -14 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -7
49x4 - 7x2 - 7x2 - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
7x2 • (7x2-1)
Add up the last 2 terms, pulling out common factors :
1 • (7x2-1)
Step-5 : Add up the four terms of step 4 :
(7x2-1) • (7x2-1)
Which is the desired factorization
Step-by-step explanation:
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