343x^3+1 factorise it
Answers
Answer:
heory : 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 : 1 is the cube of 1
Check : x3 is the cube of x1
Factorization is :
(7x - 1) • (49x2 + 7x + 1)
Trying to factor by splitting the middle term
2.2 Factoring 49x2 + 7x + 1
The first term is, 49x2 its coefficient is 49 .
The middle term is, +7x its coefficient is 7 .
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 7 .
-49 + -1 = -50
-7 + -7 = -14
-1 + -49 = -50
1 + 49 = 50
7 + 7 = 14
49 + 1 = 50
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(7x - 1) • (49x2 + 7x + 1)
Step-by-step explanation: