Answer:
will this help any, i think its the answer
Step-by-step explanation:
-4 • (x4 - 5x3 - 4x + 9)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x3" was replaced by "x^3". 2 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x•(((3•(x2))-(7•(x2)))+8))-(4•(((x4)+9)-7x3))
Step 2 :
Polynomial Roots Calculator :
2.1 Find roots (zeroes) of : F(x) = x4-7x3+9
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 9.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,9
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 17.00
-3 1 -3.00 279.00
-9 1 -9.00 11673.00
1 1 1.00 3.00
3 1 3.00 -99.00
9 1 9.00 1467.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step 2 :
(2x•(((3•(x2))-(7•(x2)))+8))-4•(x4-7x3+9)
Step 3 :
Equation at the end of step 3 :
(2x•(((3•(x2))-7x2)+8))-4•(x4-7x3+9)
Step 4 :
Equation at the end of step 4 :
(2x•((3x2-7x2)+8))-4•(x4-7x3+9)
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
8 - 4x2 = -4 • (x2 - 2)
Trying to factor as a Difference of Squares :
6.2 Factoring: x2 - 2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 2 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 6 :
-8x • (x2 - 2) - 4 • (x4 - 7x3 + 9)
Step 7 :
Step 8 :
Pulling out like terms :
8.1 Pull out like factors :
-4x4 + 20x3 + 16x - 36 =
-4 • (x4 - 5x3 - 4x + 9)
Checking for a perfect cube :
8.2 x4 - 5x3 - 4x + 9 is not a perfect cube
Trying to factor by pulling out :
8.3 Factoring: x4 - 5x3 - 4x + 9
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -4x + 9
Group 2: x4 - 5x3
Pull out from each group separately :
Group 1: (-4x + 9) • (1) = (4x - 9) • (-1)
Group 2: (x - 5) • (x3)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
8.4 Find roots (zeroes) of : F(x) = x4 - 5x3 - 4x + 9
See theory in step 2.1
In this case, the Leading Coefficient is 1 and the Trailing Constant is 9.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,9
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 19.00
-3 1 -3.00 237.00
-9 1 -9.00 10251.00
1 1 1.00 1.00
3 1 3.00 -57.00
9 1 9.00 2889.00
Polynomial Roots Calculator found no rational roots
