12m2 + 2m + 3
—————————
6m
Step-by-step explanation:
Step 1 :
1
Simplify —
3
Equation at the end of step 1 :
4 1
(2m + — ÷ m) + —
8 3
Step 2 :
1
Simplify —
2
Equation at the end of step 2 :
1 1
(2m + — ÷ m) + —
2 3
Step 3 :
1
Divide — by m
2
Equation at the end of step 3 :
1 1
(2m + ——) + —
2m 3
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 2m as the denominator :
2m 2m • 2m
2m = —— = ———————
1 2m
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2m • 2m + 1 4m2 + 1
——————————— = ———————
2m 2m
Equation at the end of step 4 :
(4m2 + 1) 1
————————— + —
2m 3
Step 5 :
Polynomial Roots Calculator :
5.1 Find roots (zeroes) of : F(m) = 4m2+1
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 4 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1
Let us test
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 5.00
-1 2 -0.50 2.00
-1 4 -0.25 1.25
1 1 1.00 5.00
1 2 0.50 2.00
1 4 0.25 1.25
Polynomial Roots Calculator found no rational roots
Calculating the Least Common Multiple :
5.2 Find the Least Common Multiple
The left denominator is : 2m
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2101
3011
Product of all
Prime Factors 236
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
m 101
Least Common Multiple:
6m
Calculating Multipliers :
5.3 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 3
Right_M = L.C.M / R_Deno = 2m
Making Equivalent Fractions :
5.4 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (4m2+1) • 3
—————————————————— = ———————————
L.C.M 6m
R. Mult. • R. Num. 2m
—————————————————— = ——
L.C.M 6m
Adding fractions that have a common denominator :
5.5 Adding up the two equivalent fractions
(4m2+1) • 3 + 2m 12m2 + 2m + 3
———————————————— = —————————————
6m 6m
Trying to factor by splitting the middle term
5.6 Factoring 12m2 + 2m + 3
The first term is, 12m2 its coefficient is 12 .
The middle term is, +2m its coefficient is 2 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant 12 • 3 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is 2 .
-36 + -1 = -37
-18 + -2 = -20
-12 + -3 = -15
-9 + -4 = -13
-6 + -6 = -12
-4 + -9 = -13
For tidiness, printing of 12 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
12m2 + 2m + 3
—————————————
6m
Processing ends successfully
plz mark em as brainliest :)
