### (3x^2-2x+5)-(x^2+3x-2)x1/2x^2

This faces reducing fountain to their lowest terms.

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## Step by step Solution ### Reformatting the entry :

Changes made to your input need to not impact the solution: (1): "x1" was replaced by "x^1".

## Step 1 :

x simplify — 2Equation at the finish of action 1 : x (((3•(x2))-2x)+5)-(((((x2)+3x)-2)•—)•x2) 2

## Step 2 :

Trying to factor by separating the middle term2.1Factoring x2+3x-2 The very first term is, x2 that coefficient is 1.The middle term is, +3x that is coefficient is 3.The critical term, "the constant", is -2Step-1 : multiply the coefficient that the very first term through the constant 1•-2=-2Step-2 : uncover two factors of -2 who sum equates to the coefficient of the middle term, i beg your pardon is 3.

 -2 + 1 = -1 -1 + 2 = 1

Observation : No 2 such components can be discovered !! Conclusion : Trinomial have the right to not it is in factored

Equation in ~ the finish of action 2 :

x•(x2+3x-2) (((3•(x2))-2x)+5)-(———————————•x2) 2

## Step 3 :

Multiplying exponential expression :3.1 x1 multiplied by x2 = x(1 + 2) = x3

Equation in ~ the finish of step 3 :

x3•(x2+3x-2) (((3•(x2))-2x)+5)-———————————— 2

## step 4 :

Equation in ~ the end of action 4 : x3 • (x2 + 3x - 2) ((3x2 - 2x) + 5) - —————————————————— 2

## Step 5 :

Rewriting the totality as an Equivalent portion :5.1Subtracting a fraction from a whole Rewrite the entirety as a portion using 2 as the denominator :

3x2 - 2x + 5 (3x2 - 2x + 5) • 2 3x2 - 2x + 5 = ———————————— = —————————————————— 1 2 Equivalent portion : The portion thus produced looks different yet has the very same value as the whole typical denominator : The equivalent portion and the other fraction involved in the calculation re-publishing the same denominator

Trying to element by separating the center term

5.2Factoring 3x2 - 2x + 5 The very first term is, 3x2 that is coefficient is 3.The center term is, -2x that is coefficient is -2.The critical term, "the constant", is +5Step-1 : main point the coefficient that the very first term through the continuous 3•5=15Step-2 : find two factors of 15 whose sum equates to the coefficient that the middle term, i beg your pardon is -2.

 -15 + -1 = -16 -5 + -3 = -8 -3 + -5 = -8 -1 + -15 = -16 1 + 15 = 16 3 + 5 = 8 5 + 3 = 8 15 + 1 = 16

Observation : No 2 such determinants can be discovered !! Conclusion : Trinomial can not be factored

Adding fountain that have a typical denominator :

5.3 including up the two equivalent fractions include the two tantamount fractions which now have actually a common denominatorCombine the numerators together, placed the sum or difference over the typical denominator then minimize to lowest state if possible:

(3x2-2x+5) • 2 - (x3 • (x2+3x-2)) -x5 - 3x4 + 2x3 + 6x2 - 4x + 10 ————————————————————————————————— = ——————————————————————————————— 2 2 do the efforts to aspect by pulling the end :5.4 Factoring: -x5 - 3x4 + 2x3 + 6x2 - 4x + 10 Thoughtfully split the expression at hand into groups, each group having 2 terms:Group 1: 2x3 + 6x2Group 2: -x5 - 3x4Group 3: -4x + 10Pull out from each team separately :Group 1: (x + 3) • (2x2)Group 2: (x + 3) • (-x4)Group 3: (2x - 5) • (-2) looking for common sub-expressions : group 1: (x + 3) • (2x2)Group 2: (x + 3) • (-x4) team 3: (2x - 5) • (-2) (1) + (2):(x + 3) • (2x2 - x4) negative news !! Factoring by pulling out falls short : The groups have no typical factor and can not be added up to type a multiplication.

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### Polynomial roots Calculator :

5.5 discover roots (zeroes) the : F(x) = -x5 - 3x4 + 2x3 + 6x2 - 4x + 10Polynomial roots Calculator is a collection of methods aimed at finding worths ofxfor i m sorry F(x)=0 Rational roots Test is just one of the above mentioned tools. It would only uncover Rational Roots the is number x which can be expressed together the quotient of two integersThe Rational root Theorem states that if a polynomial zeroes for a reasonable numberP/Q then ns is a factor of the Trailing continuous and Q is a variable of the top CoefficientIn this case, the top Coefficient is -1 and the Trailing constant is 10. The factor(s) are: the the top Coefficient : 1of the Trailing constant : 1 ,2 ,5 ,10 Let united state test ....

PQP/QF(P/Q)Divisor
-11 -1.00 16.00
-21 -2.00 10.00
-51 -5.00 1180.00
-101-10.0068650.00
11 1.00 10.00
21 2.00 -38.00
51 5.00-4610.00
101 10.00-127430.00

Polynomial roots Calculator discovered no rational root

## Final result :

+x5 + 3x4 + 2x3 + 6x2 + 4x + 10 ——————————————————————————————— 2