Respuesta :
Answer:
I'm pretty sure that this one is the correct factorization of the polynomial above: c) (3x+4)(9x^2-12x+16)
(3x−4)⋅(9x
2
+12x+16)
See steps
Step by Step Solution:
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STEP
1
:
Equation at the end of step 1
33x3 - 64
STEP
2
:
Trying to factor as a Difference of Cubes
2.1 Factoring: 27x3-64
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 : 27 is the cube of 3
Check : 64 is the cube of 4
Check : x3 is the cube of x1
Factorization is :
(3x - 4) • (9x2 + 12x + 16)
Trying to factor by splitting the middle term
2.2 Factoring 9x2 + 12x + 16
The first term is, 9x2 its coefficient is 9 .
The middle term is, +12x its coefficient is 12 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 9 • 16 = 144
Step-2 : Find two factors of 144 whose sum equals the coefficient of the middle term, which is 12 .
-144 + -1 = -145
-72 + -2 = -74
-48 + -3 = -51
-36 + -4 = -40
-24 + -6 = -30
-18 + -8 = -26
For tidiness, printing of 24 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(3x - 4) • (9x2 + 12x + 16)
Answer:
C
Step-by-step explanation:
When factorising the sum of cubes, we use the formula
a^3+b^3=(a+b)(a^2−ab+b^2).
In this case of 27x3+64,
27x^3=a^3
64=b^3
Find a:
27x^3=a^3
3^√27x^3=3^√a^3
3x=a
Find b:
64=b^3
3^√64=3√b^3
4=b
Substitute a=3x and b=4 into
(a+b)(a^2−ab+b^2)
(3x+4)((3x)^2−(3x×4)+4^2)
= (3x+4)(9x^2−12x+16)
(3x+4)(9x^2−12x+16) is the factorised form of 27x^3+64
