Mathematics, 10.10.2019 20:30 kealalac1

Factor a 3 - 3 + 3a 2 - a. (a - 1)(a + 1)(a + 3) (a2 + 1)(a - 3) (a2 - 3)(a + 1)

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Changes made to your input should not affect the solution:

(1): "a2" was replaced by "a^2". 2 more similar replacement(s).

(2): Dot was discarded near "a.(".

Step by step solution :
Step 1  : (0+(3•(a2)))-a•(a-1)•(a+1))•(a+3))•(a2+1))•(a-3))•(a2-3))•(a+1))

Step  2  : (0+(3•(a2)))-a•(a-1)•(a+1)•(a+3))•(a2+1))•(a-3))•(a2-3))•(a+1))

Step  3  : (0+(3•(a2)))-a•(a-1)•(a+1)•(a+3)•(a2+1))•(a-3))•(a2-3))•(a+1))

Step  4  :Polynomial Roots Calculator :

Find roots (zeroes) of :       F(a) = a2+1
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  1.

The factor(s) are:

of the Leading Coefficient :  1
of the Trailing Constant :  1

Let us test

P Q P/Q F(P/Q) Divisor -1 1 -1.00 2.00 1 1 1.00 2.00

Polynomial Roots Calculator found no rational roots

step  4  : (0+(3•(a2)))-(((a•(a-1)•(a+1)•(a+3)•(a2+1)•(a-3))•(a2-3))•(a+1))

step  5  : (0+(3•(a2)))-((a•(a-1)•(a+1)•(a+3)•(a2+1)•(a-3)•(a2-3))•(a+1))

Step  6  :Trying to factor as a Difference of Squares :

Factoring:  a2-3

(Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B) )

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 =
         A2 - B2

(Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.)

Check : 3 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

step 6 : (0+(3•(a2)))-(a•(a-1)•(a+1)•(a+3)•(a2+1)•(a-3)•(a2-3)•(a+1))

Step 7 :Evaluate an expression :

Multiply  (a+1) by  (a+1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (a+1) and the exponents are :
          1 , as  (a+1) is the same number as  (a+1)1
and   1 , as  (a+1) is the same number as  (a+1)1
The product is therefore,  (a+1)(1+1) = (a+1)2

step 7  : (0+(3•(a2)))-a•(a-1)•(a+1)2•(a+3)•(a2+1)•(a-3)•(a2-3)

Step 8 : (0+3a2)-a•(a-1)•(a+1)2•(a+3)•(a2+1)•(a-3)•(a2-3)

Step  9  : Evaluate : (a+1)2 = a2+2a+1

Step  10  :Pulling out like terms :

Pull out like factors :

-a10 - a9 + 12a8 + 12a7 - 26a6 - 26a5 - 12a4 - 12a3 + 30a2 + 27a =

-a • (a9 + a8 - 12a7 - 12a6 + 26a5 + 26a4 + 12a3 + 12a2 - 30a - 27)

Final result : -a • (a9 + a8 - 12a7 - 12a6 + 26a5 + 26a4 + 12a3 + 12a2 - 30a - 27)
hoped this helped

Answer from: Quest

Dis the correct answer

Answer from: Quest

its kind of blurry. can you put a clearer pic?

step-by-step explanation:

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Factor a 3 - 3 + 3a 2 - a. (a - 1)(a + 1)(a + 3) (a2 + 1)(a - 3) (a2 - 3)(a + 1)...