Find the factor of p3+8
Answers
Answer:
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Step-by-step explanation:
Theory : A sum 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 : 8 is the cube of 2
Check : p3 is the cube of p1
Factorization is :
(p + 2) • (p2 - 2p + 4)
Trying to factor by splitting the middle term
1.2 Factoring p2 - 2p + 4
The first term is, p2 its coefficient is 1 .
The middle term is, -2p its coefficient is -2 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -2 .
-4 + -1 = -5
-2 + -2 = -4
-1 + -4 = -5
1 + 4 = 5
2 + 2 = 4
4 + 1 = 5
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(p + 2) • (p2 - 2p + 4)