Answer:
(7x - 3) • (49x2 + 21x + 9)
Explanation:
STEP
1
:
Equation at the end of step 1
73x3 - 27
STEP
2
:
Trying to factor as a Difference of Cubes:
2.1 Factoring: 343x3-27
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0-b3 =
a3-b3
Check : 343 is the cube of 7
Check : 27 is the cube of 3
Check : x3 is the cube of x1
Factorization is :
(7x - 3) • (49x2 + 21x + 9)
Trying to factor by splitting the middle term
2.2 Factoring 49x2 + 21x + 9
The first term is, 49x2 its coefficient is 49 .
The middle term is, +21x its coefficient is 21 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 49 • 9 = 441
Step-2 : Find two factors of 441 whose sum equals the coefficient of the middle term, which is 21 .
-441 + -1 = -442
-147 + -3 = -150
-63 + -7 = -70
-49 + -9 = -58
-21 + -21 = -42
-9 + -49 = -58
For tidiness, printing of 12 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored