(d) (M2+4m-21) (M-3)
Answers
Answer:
2M^24m^2-21m-6m-12m+61
Answer:
mm3+4m2−3m−21
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "m2" was replaced by "m^2".
STEP1:
21 Simplify —— m
Equation at the end of step1:
21 (((m2) + 4m) - ——) - 3 m
STEP2:Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using m as the denominator :
m2 + 4m (m2 + 4m) • m m2 + 4m = ——————— = ————————————— 1 m
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
STEP3:Pulling out like terms
3.1 Pull out like factors :
m2 + 4m = m • (m + 4)
Adding fractions that have a common denominator :
3.2 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:
m • (m+4) • m - (21) m3 + 4m2 - 21 ———————————————————— = ————————————— m m
Equation at the end of step3:
(m3 + 4m2 - 21) ——————————————— - 3 m
STEP4:Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using m as the denominator :
3 3 • m 3 = — = ————— 1 m
Polynomial Roots Calculator :
4.2 Find roots (zeroes) of : F(m) = m3 + 4m2 - 21
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 1 and the Trailing Constant is -21.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,7 ,21
Let us test ....
P Q P/Q F(P/Q) Divisor -1 1 -1.00 -18.00 -3 1 -3.00 -12.00 -7 1 -7.00 -168.00 -21 1 -21.00 -7518.00 1 1 1.00 -16.00 3 1 3.00 42.00 7 1 7.00 518.00 21 1 21.00 11004.00
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
4.3 Adding up the two equivalent fractions
(m3+4m2-21) - (3 • m) m3 + 4m2 - 3m - 21 ————————————————————— = —————————————————— m m
Checking for a perfect cube :
4.4 m3 + 4m2 - 3m - 21 is not a perfect cube
Trying to factor by pulling out :
4.5 Factoring: m3 + 4m2 - 3m - 21
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -3m - 21
Group 2: m3 + 4m2
Pull out from each group separately :
Group 1: (m + 7) • (-3)
Group 2: (m + 4) • (m2)
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 :
4.6 Find roots (zeroes) of : F(m) = m3 + 4m2 - 3m - 21
See theory in step 4.2
In this case, the Leading Coefficient is 1 and the Trailing Constant is -21.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,7 ,21
Let us test ....
P Q P/Q F(P/Q) Divisor -1 1 -1.00 -15.00 -3 1 -3.00 -3.00 -7 1 -7.00 -147.00 -21 1 -21.00 -7455.00 1 1 1.00 -19.00 3 1 3.00 33.00 7 1 7.00 497.00 21 1 21.00 10941.00
Polynomial Roots Calculator found no rational roots
Final result :
m3 + 4m2 - 3m - 21