Answer:
STEP1:
4 Simplify — 1
Equation at the end of step1:
4 (((((((2•(a3))+(4•(a2)))-2a)-————)-(4•(a2)))-4a)+16)•(((((a2)-6a)+(4•a2))+2a)-4) (a3)
STEP2:Equation at the end of step 2
4 (((((((2•(a3))+(4•(a2)))-2a)-————)-(4•(a2)))-4a)+16)•(((((a2)-6a)+22a2)+2a)-4) (a3)
STEP 3 :
Equation at the end of step3:
4 (((((((2•(a3))+(4•(a2)))-2a)-————)-22a2)-4a)+16)•(5a2-4a-4) (a3)
STEP 4 :
4 Simplify —— a3
Equation at the end of step4:
4 (((((((2•(a3))+(4•(a2)))-2a)-——)-22a2)-4a)+16)•(5a2-4a-4) a3
STEP 5 :
Equation at the end of step5:
4 (((((((2•(a3))+22a2)-2a)-——)-22a2)-4a)+16)•(5a2-4a-4) a3
STEP 6 :
Equation at the end of step6:
4 ((((((2a3+22a2)-2a)-——)-22a2)-4a)+16)•(5a2-4a-4) a3
STEP7:Rewriting the whole as an Equivalent Fraction
7.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using a3 as the denominator :
2a3 + 4a2 - 2a (2a3 + 4a2 - 2a) • a3 2a3 + 4a2 - 2a = —————————————— = ————————————————————— 1 a3
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
STEP8:Pulling out like terms
8.1 Pull out like factors :
2a3 + 4a2 - 2a = 2a • (a2 + 2a - 1)
Trying to factor by splitting the middle term
8.2 Factoring a2 + 2a - 1
The first term is, a2 its coefficient is 1 .
The middle term is, +2a its coefficient is 2 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 1 • -1 = -1
Step-2 : Find two factors of -1 whose sum equals the coefficient of the middle term, which is 2 .
-1 + 1 = 0
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Adding fractions that have a common denominator :
8.3 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:
2a • (a2+2a-1) • a3 - (4) 2a6 + 4a5 - 2a4 - 4 ————————————————————————— = ——————————————————— a3 a3
Equation at the end of step8:
(2a6+4a5-2a4-4) (((———————————————-22a2)-4a)+16)•(5a2-4a-4) a3
STEP9:
Rewriting the whole as an Equivalent Fraction :
9.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using a3 as the denominator :
22a2 22a2 • a3 22a2 = ———— = ————————— 1 a3
STEP10:
Pulling out like terms :
10.1 Pull out like factors :
2a6 + 4a5 - 2a4 - 4 =
2 • (a6 + 2a5 - a4 - 2)
Checking for a perfect cube :
10.2 a6 + 2a5 - a4 - 2 is not a perfect cube
Trying to factor by pulling out :
10.3 Factoring: a6 + 2a5 - a4 - 2
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -a4 - 2
Group 2: a6 + 2a5
Pull out from each group separately :
Group 1: (a4 + 2) • (-1)
Group 2: (a + 2) • (a5)
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 :
10.4 Find roots (zeroes) of : F(a) = a6 + 2a5 - a4 - 2
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a 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 -2.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant :
