Answer:
(3v5+8v3+10v2)+(-12v5+4v3+14v2)
Final result :
-3v2 • (3v3 - 4v - 8)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(12•(v5)))+(4•(v3)))+(2•7v2))
Step 2 :
Equation at the end of step 2 :
(((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(12•(v5)))+22v3)+(2•7v2))
Step 3 :
Equation at the end of step 3 :
(((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(22•3v5))+22v3)+(2•7v2))
Step 4 :
Equation at the end of step 4 :
(((3•(v5))+(8•(v3)))+(2•5v2))+(-12v5+4v3+14v2)
Step 5 :
Equation at the end of step 5 :
(((3•(v5))+23v3)+(2•5v2))+(-12v5+4v3+14v2)
Step 6 :
Equation at the end of step 6 :
((3v5 + 23v3) + (2•5v2)) + (-12v5 + 4v3 + 14v2)
Step 7 :
Step 8 :
Pulling out like terms :
8.1 Pull out like factors :
-9v5 + 12v3 + 24v2 = -3v2 • (3v3 - 4v - 8)
Polynomial Roots Calculator :
8.2 Find roots (zeroes) of : F(v) = 3v3 - 4v - 8
Polynomial Roots Calculator is a set of methods aimed at finding values of v for which F(v)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers v 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 3 and the Trailing Constant is -8.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1 ,2 ,4 ,8
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -7.00
-1 3 -0.33 -6.78
-2 1 -2.00 -24.00
-2 3 -0.67 -6.22
-4 1 -4.00 -184.00
-4 3 -1.33 -9.78
-8 1 -8.00 -1512.00
-8 3 -2.67 -54.22
1 1 1.00 -9.00
1 3 0.33 -9.22
2 1 2.00 8.00
2 3 0.67 -9.78
4 1 4.00 168.00
4 3 1.33 -6.22
8 1 8.00 1496.00
8 3 2.67 38.22
Polynomial Roots Calculator found no rational roots
Final result :
-3v2 • (3v3 - 4v - 8)
Step-by-step explanation:
