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2x(3x2- 7x²+ 8) - 4(x4+9 - 7x3)

1 Answer

4 votes

Answer:

will this help any, i think its the answer

Explanation:

-4 • (x4 - 5x3 - 4x + 9)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x3" was replaced by "x^3". 2 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(2x•(((3•(x2))-(7•(x2)))+8))-(4•(((x4)+9)-7x3))

Step 2 :

Polynomial Roots Calculator :

2.1 Find roots (zeroes) of : F(x) = x4-7x3+9

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 9.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,3 ,9

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 17.00

-3 1 -3.00 279.00

-9 1 -9.00 11673.00

1 1 1.00 3.00

3 1 3.00 -99.00

9 1 9.00 1467.00

Polynomial Roots Calculator found no rational roots

Equation at the end of step 2 :

(2x•(((3•(x2))-(7•(x2)))+8))-4•(x4-7x3+9)

Step 3 :

Equation at the end of step 3 :

(2x•(((3•(x2))-7x2)+8))-4•(x4-7x3+9)

Step 4 :

Equation at the end of step 4 :

(2x•((3x2-7x2)+8))-4•(x4-7x3+9)

Step 5 :

Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

8 - 4x2 = -4 • (x2 - 2)

Trying to factor as a Difference of Squares :

6.2 Factoring: x2 - 2

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 : 2 is not a square !!

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

Equation at the end of step 6 :

-8x • (x2 - 2) - 4 • (x4 - 7x3 + 9)

Step 7 :

Step 8 :

Pulling out like terms :

8.1 Pull out like factors :

-4x4 + 20x3 + 16x - 36 =

-4 • (x4 - 5x3 - 4x + 9)

Checking for a perfect cube :

8.2 x4 - 5x3 - 4x + 9 is not a perfect cube

Trying to factor by pulling out :

8.3 Factoring: x4 - 5x3 - 4x + 9

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -4x + 9

Group 2: x4 - 5x3

Pull out from each group separately :

Group 1: (-4x + 9) • (1) = (4x - 9) • (-1)

Group 2: (x - 5) • (x3)

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 :

8.4 Find roots (zeroes) of : F(x) = x4 - 5x3 - 4x + 9

See theory in step 2.1

In this case, the Leading Coefficient is 1 and the Trailing Constant is 9.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,3 ,9

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 19.00

-3 1 -3.00 237.00

-9 1 -9.00 10251.00

1 1 1.00 1.00

3 1 3.00 -57.00

9 1 9.00 2889.00

Polynomial Roots Calculator found no rational roots

User Alfred Rossi
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