Respuestas
Explicación paso a paso:
x6-10x3+25
Final result :
(x3 - 5)2
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x3" was replaced by "x^3". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((x6) - (2•5x3)) + 25
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring x6-10x3+25
The first term is, x6 its coefficient is 1 .
The middle term is, -10x3 its coefficient is -10 .
The last term, "the constant", is +25
Step-1 : Multiply the coefficient of the first term by the constant 1 • 25 = 25
Step-2 : Find two factors of 25 whose sum equals the coefficient of the middle term, which is -10 .
-25 + -1 = -26
-5 + -5 = -10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -5
x6 - 5x3 - 5x3 - 25
Step-4 : Add up the first 2 terms, pulling out like factors :
x3 • (x3-5)
Add up the last 2 terms, pulling out common factors :
5 • (x3-5)
Step-5 : Add up the four terms of step 4 :
(x3-5) • (x3-5)
Which is the desired factorization
Trying to factor as a Difference of Cubes:
2.2 Factoring: x3-5
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 : 5 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Polynomial Roots Calculator :
2.3 Find roots (zeroes) of : F(x) = x3-5
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -6.00
-5 1 -5.00 -130.00
1 1 1.00 -4.00
5 1 5.00 120.00
Polynomial Roots Calculator found no rational roots
Trying to factor as a Difference of Cubes:
2.4 Factoring: x3-5
Check : 5 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Polynomial Roots Calculator :
2.5 Find roots (zeroes) of : F(x) = x3-5
See theory in step 2.3
In this case, the Leading Coefficient is 1 and the Trailing Constant is -5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -6.00
-5 1 -5.00 -130.00
1 1 1.00 -4.00
5 1 5.00 120.00
Polynomial Roots Calculator found no rational roots
Multiplying Exponential Expressions :
2.6 Multiply (x3-5) by (x3-5)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x3-5) and the exponents are :
1 , as (x3-5) is the same number as (x3-5)1
and 1 , as (x3-5) is the same number as (x3-5)1
The product is therefore, (x3-5)(1+1) = (x3-5)2
Final result :
(x3 - 5)2
Explicación paso a paso:
x⁶+10x³+25
x³. 5
2(x³+5)
(x³+5)²