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The answer below does find one root, and finding roots is one way to discover factors. But it does not find the complete factorization. x = -3/2 is also a root of the stated 'equation'. So two of the factors are (2x - 3) and (2x + 3). Then long division could be used to find remaining factor(s).
Recall that a2 - b2 = (a + b)(a - b). Let a2 = 16x4, and b2 = 81.
so, a = 4x2 and b = 9.
So: 16x4 - 81 = (4x2 + 9)(4x2 - 9), and (4x2 - 9) factors to (2x + 3)(2x - 3).
So the factorization is: (4x2 + 9)(2x + 3)(2x - 3).
With complex: (2x + 3i)(2x - 3i)(2x + 3)(2x - 3), where i = sqrt(-1)
So the other two roots are: 3i/2 and -3i/2
Finding a root:
16X^4 - 81 = 0
add 81 to each side : 16X^4 = 81
divide both sides by 16, leave as fraction
X^4 = 81/16
take 4th root both sides
X = 4root(81/16)
this can be expressed as.........
X = 4root(81)/4root(16)
X = 3/2 [indicates (2x - 3) is one of the factors]
check
16(3/2)^4 - 81 = 0
16 * 81/16 - 81 = 0
0 = 0
checks
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∙ 13y ago
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How do you factor the expression 64x cubed minus 27?
(4x - 3)(16x^2 + 12x + 9)
What are the greatest common factor of 16x and 36x?
Greatest common factor of 16x and 36x is 4x.
What is the greatest common factor of the terms in the polynomial 4x4 plus 16x?
The GCF is 4x.
How do you factor 12x2 16x 5?
4x2(4x3 + 3)
What is the greatest common factor of 16x squaredand 56x?
The GCF is 8x.
How do you factor 64x to the third power minus 27y to the third power?
(4x - 3y)(16x^2 + 12xy + 9y^2)
How do you factor 5x to the second power minus 16x plus 12?
5x2-16x+12 = (5x-6)(x-2) when factored with the help of the quadratic equation formula
How do you factor X cubed plus 4 x squared minus 16x minus 64?
x3 + 4x2 - 16x - 64 = (x + 4)(x + 4)(x - 4).
What is the LCM of 16X and 32X to the fourth power?
Note that 16X is a factor of 32X [16X times 2 is 32X]. So now whether it's (32X)^4 or 32 times (X^4), that will still be the LCM, so the answer is 32X to the 4th power, just as it's stated in the question.
How do you factor the expression 64x cubed minus 27?
(4x - 3)(16x^2 + 12x + 9)
How do you factor 2x squared minus 16x plus 14?
2(x - 7)(x - 1)
Factor 64x to the third power minus 27x to the third power?
In case you meant 64x^3 - 27y^3, that factors to (4x - 3y)(16x^2 + 12xy + 9y^2)
What is the greatest common factor of 16x to the third power-6x to the second power 2x?
The GCF is 2x.
How do you factor 64 x cubed minus y cubed?
64 x cubed minus y cubed is (4x - y)(16x^2 + 4xy + y^2)
How do you factor x squared plus 16x minus 348?
x2 + 16x - 348 cannot be factored. Solving for x with the quadratic formula results in x = -8 - 2√103 and x = -8 + 2√103
How do you factor x3 plus 5x2 minus 16x minus 80?
To factorise x3 + 5x2 - 16x - 80 I note that -80 = 5 x -16 and 5 & -16 are the coefficients of x2 and x. Thus I have: x3 + 5x2 - 16x - 80 = (x + 5)(x2 - 16) and the second term is a difference of 2 squares, meaning I have: x3 + 5x2 - 16x - 80 = (x + 5)(x + 4)(x - 4)
What are the greatest common factor of 16x and 36x?
Greatest common factor of 16x and 36x is 4x.
