x^3+6x^2-5x by (x-2) by long division method
Answers
Answer:
x • (x3 + 4x2 - 12x - 5)
————————————————————————
x - 2
Step by step solution :
Step 1 :
x
Simplify —————
x - 2
Equation at the end of step 1 :
x
((x3)+(6•(x2)))-(5•———)
x-2
Step 2 :
Equation at the end of step 2 :
5x
((x3) + (6 • (x2))) - —————
x - 2
Step 3 :
Equation at the end of step 3 :
5x
((x3) + (2•3x2)) - —————
x - 2
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using (x-2) as the denominator :
x3 + 6x2 (x3 + 6x2) • (x - 2)
x3 + 6x2 = ———————— = ————————————————————
1 (x - 2)
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
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
x3 + 6x2 = x2 • (x + 6)
Adding fractions that have a common denominator :
5.2 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:
x2 • (x+6) • (x-2) - (5x) x4 + 4x3 - 12x2 - 5x
————————————————————————— = ————————————————————
1 • (x-2) 1 • (x - 2)
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
x4 + 4x3 - 12x2 - 5x =
x • (x3 + 4x2 - 12x - 5)
Checking for a perfect cube :
6.2 x3 + 4x2 - 12x - 5 is not a perfect cube
Trying to factor by pulling out :
6.3 Factoring: x3 + 4x2 - 12x - 5
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3 - 5
Group 2: 4x2 - 12x
Pull out from each group separately :
Group 1: (x3 - 5) • (1)
Group 2: (x - 3) • (4x)
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(x) = x3 + 4x2 - 12x - 5
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 -5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 10.00
-5 1 -5.00 30.00
1 1 1.00 -12.00
5 1 5.00 160.00
Polynomial Roots Calculator found no rational roots
Final result :
x • (x3 + 4x2 - 12x - 5)
————————————————————————
x - 2
Answer:
hope it helps you............
