(2m--3) (5m+2) + (3m-7m)(4m-1)
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Answer:
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Step-by-step explanation:
6m^4-3m^2+m)-(2m^3+5m^2+4m)+(m^2-m)
This deals with simplification or other simple results.
Overview
Steps
Topics
1 solution(s) found
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Step by Step Solution
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STEP
1
:
Equation at the end of step 1
((((6•(m4))-(3•(m2)))+m)-(((2•(m3))+5m2)+4m))+(m2-m)
STEP
2
:
Equation at the end of step
2
:
((((6•(m4))-(3•(m2)))+m)-((2m3+5m2)+4m))+(m2-m)
STEP
3
:
Equation at the end of step
3
:
((((6•(m4))-3m2)+m)-(2m3+5m2+4m))+(m2-m)
STEP
4
:
Equation at the end of step
4
:
((((2•3m4) - 3m2) + m) - (2m3 + 5m2 + 4m)) + (m2 - m)
STEP
5
:
STEP
6
:
Pulling out like terms
6.1 Pull out like factors :
6m4 - 2m3 - 7m2 - 4m =
m • (6m3 - 2m2 - 7m - 4)
Checking for a perfect cube :
6.2 6m3 - 2m2 - 7m - 4 is not a perfect cube
Trying to factor by pulling out :
6.3 Factoring: 6m3 - 2m2 - 7m - 4
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -7m - 4
Group 2: 6m3 - 2m2
Pull out from each group separately :
Group 1: (7m + 4) • (-1)
Group 2: (3m - 1) • (2m2)
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 :
6.4 Find roots (zeroes) of : F(m) = 6m3 - 2m2 - 7m - 4
Polynomial Roots Calculator is a set of methods aimed at finding values of m for which F(m)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers m 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 6 and the Trailing Constant is -4.
The factor(s) are:
of the Leading Coefficient : 1,2 ,3 ,6
of the Trailing Constant : 1 ,2 ,4
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -5.00
-1 2 -0.50 -1.75
-1 3 -0.33 -2.11
-1 6 -0.17 -2.92
-2 1 -2.00 -46.00
-2 3 -0.67 -2.00
-4 1 -4.00 -392.00
-4 3 -1.33 -12.44
1 1 1.00 -7.00
1 2 0.50 -7.25
1 3 0.33 -6.33
1 6 0.17 -5.19
2 1 2.00 22.00
2 3 0.67 -7.78
4 1 4.00 320.00
4 3 1.33 -2.67
Polynomial Roots Calculator found no rational roots
Final result :
m • (6m3 - 2m2 - 7m - 4)