### (2x^3-9x^2+11x-6)/(x-3)

This faces finding the root (zeroes) the polynomials.

You are watching: What is the result when 2x^3-9x^2+11x-6 is divided by x-3

## Step 1 :

Equation in ~ the finish of action 1 :

## step 2 :

Equation at the end of step 2 :

## Step 3 :

2x3 - 9x2 + 11x - 6 leveling ——————————————————— x - 3 Checking because that a perfect cube :3.12x3 - 9x2 + 11x - 6 is not a perfect cube

Trying to element by pulling the end :

3.2 Factoring: 2x3 - 9x2 + 11x - 6 Thoughtfully break-up the expression at your disposal into groups, each team having 2 terms:Group 1: 11x - 6Group 2: 2x3 - 9x2Pull out from each group separately :Group 1: (11x - 6) • (1)Group 2: (2x - 9) • (x2)Bad news !! Factoring through pulling out falls short : The teams have no usual factor and can not be added up to kind a multiplication.

### Polynomial root Calculator :

3.3 find roots (zeroes) of : F(x) = 2x3 - 9x2 + 11x - 6Polynomial root Calculator is a set of approaches aimed in ~ finding worths ofxfor which F(x)=0 Rational root Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which have the right to be expressed as the quotient of 2 integersThe Rational source Theorem claims that if a polynomial zeroes because that a reasonable numberP/Q then p is a aspect of the Trailing consistent and Q is a variable of the top CoefficientIn this case, the top Coefficient is 2 and the Trailing continuous is -6. The factor(s) are: of the top Coefficient : 1,2 the the Trailing consistent : 1 ,2 ,3 ,6 Let us test ....

PQP/QF(P/Q)Divisor
-11 -1.00 -28.00
-12 -0.50 -14.00
-21 -2.00 -80.00
-31 -3.00 -174.00
-32 -1.50 -49.50
-61 -6.00 -828.00
11 1.00 -2.00
12 0.50 -2.50
21 2.00 -4.00
31 3.00 0.00x - 3
32 1.50 -3.00
61 6.00 168.00

The variable Theorem says that if P/Q is root of a polynomial climate this polynomial can be separated by q*x-p note that q and p originate indigenous P/Q lessened to the lowest terms In our case this way that 2x3 - 9x2 + 11x - 6can be divided with x - 3

### Polynomial Long department :

3.4 Polynomial Long division dividing : 2x3 - 9x2 + 11x - 6("Dividend") By:x - 3("Divisor")

 dividend 2x3 - 9x2 + 11x - 6 -divisor * 2x2 2x3 - 6x2 remainder - 3x2 + 11x - 6 -divisor * -3x1 - 3x2 + 9x remainder 2x - 6 -divisor * 2x0 2x - 6 remainder 0

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

Trying to aspect by separating the center term

3.5Factoring 2x2-3x+2 The very first term is, 2x2 that coefficient is 2.The center term is, -3x its coefficient is -3.The critical term, "the constant", is +2Step-1 : main point the coefficient of the an initial term by the consistent 2•2=4Step-2 : find two components of 4 who sum equals the coefficient the the center term, which is -3.

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 -4 + -1 = -5 -2 + -2 = -4 -1 + -4 = -5 1 + 4 = 5 2 + 2 = 4 4 + 1 = 5

Observation : No 2 such components can be found !! Conclusion : Trinomial have the right to not be factored

Canceling out :

3.6 Cancel the end (x-3) which shows up on both political parties of the fraction line.