Mathematics, 19.01.2020 08:31 lilanth66

Simplify the polynomial

(2x^3 + x^2 - 4x) - (9x^3 + - 3x^2)

Answers: 3

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Answer from: yqui8767

(2x3-4x2-3x-9)/(x-3) Final result : 2x2 + 2x + 3 Step by step solution :Step 1 :Equation at the end of step 1 : Step 2 :Equation at the end of step 2 : Step 3 : 2x3 - 4x2 - 3x - 9 Simplify —————————————————— x - 3 Checking for a perfect cube :

3.1 2x3 - 4x2 - 3x - 9 is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  2x3 - 4x2 - 3x - 9

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

Group 1:  -3x - 9
Group 2:  2x3 - 4x2

Pull out from each group separately :

Group 1:   (x + 3) • (-3)
Group 2:   (x - 2) • (2x2)

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 :

3.3    Find roots (zeroes) of :       F(x) = 2x3 - 4x2 - 3x - 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  2  and the Trailing Constant is  -9.

The factor(s) are:

of the Leading Coefficient :  1,2
of the Trailing Constant :  1 ,3 ,9

Let us test

P Q P/Q F(P/Q) Divisor -1 1 -1.00 -12.00 -1 2 -0.50 -8.75 -3 1 -3.00 -90.00 -3 2 -1.50 -20.25 -9 1 -9.00 -1764.00 -9 2 -4.50 -258.75 1 1 1.00 -14.00 1 2 0.50 -11.25 3 1 3.00 0.00 x - 3 3 2 1.50 -15.75 9 1 9.00 1098.00 9 2 4.50 78.75

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that
2x3 - 4x2 - 3x - 9
can be divided with x - 3

Polynomial Long Division :

3.4    Polynomial Long Division
Dividing :  2x3 - 4x2 - 3x - 9
                              ("Dividend")
By         :    x - 3    ("Divisor")

dividend 2x3 - 4x2 - 3x - 9 - divisor * 2x2 2x3 - 6x2 remainder 2x2 - 3x - 9 - divisor * 2x1 2x2 - 6x remainder 3x - 9 - divisor * 3x0 3x - 9 remainder 0

Quotient : 2x2+2x+3 Remainder: 0

Trying to factor by splitting the middle term

3.5     Factoring  2x2+2x+3

The first term is,  2x2  its coefficient is  2 .
The middle term is,  +2x  its coefficient is  2 .
The last term, "the constant", is  +3

Step-1 : Multiply the coefficient of the first term by the constant   2 • 3 = 6

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   2 .

-6 + -1 = -7 -3 + -2 = -5 -2 + -3 = -5 -1 + -6 = -7 1 + 6 = 7 2 + 3 = 5 3 + 2 = 5 6 + 1 = 7

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Canceling Out :

3.6 Cancel out (x-3) which appears on both sides of the fraction line.

Final result : 2x2 + 2x + 3

Answer from: Quest

a and c

step-by-step explanation:

Answer from: Quest

125 yards

step-by-step explanation:

i take 75 plus 50.

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