### (x4-3x2+4x-3)/(x2+x-3)

This deals with simplification or other simple results.

You are watching: The quotient of (x4 – 3x2 + 4x – 3) and a polynomial is (x2 + x – 3). what is the polynomial?

## Step by Step Solution ### Reformatting the input :

Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". 2 more similar replacement(s).

## Step 1 :

Equation at the end of step 1 :

## Step 2 :

x4 - 3x2 + 4x - 3 Simplify ————————————————— x2 + x - 3 Checking for a perfect cube :2.1x4 - 3x2 + 4x - 3 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x4 - 3x2 + 4x - 3 Thoughtfully split the expression at hand into groups, each group having two terms:Group 1: 4x - 3Group 2: x4 - 3x2Pull out from each group separately :Group 1: (4x - 3) • (1)Group 2: (x2 - 3) • (x2)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 :

2.3 Find roots (zeroes) of : F(x) = x4 - 3x2 + 4x - 3Polynomial Roots Calculator is a set of methods aimed at finding values ofxfor 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 integersThe Rational Root Theorem states that if a polynomial zeroes for a rational numberP/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 and the Trailing Constant is -3. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 ,3 Let us test ....

PQP/QF(P/Q)Divisor
-11 -1.00 -9.00
-31 -3.00 39.00
11 1.00 -1.00
31 3.00 63.00

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term

2.4Factoring x2 + x - 3 The first term is, x2 its coefficient is 1.The middle term is, +x its coefficient is 1.The last term, "the constant", is -3Step-1 : Multiply the coefficient of the first term by the constant 1•-3=-3Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 1.

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 -3 + 1 = -2 -1 + 3 = 2

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

### Polynomial Long Division :

2.5 Polynomial Long Division Dividing : x4-3x2+4x-3("Dividend") By:x2+x-3("Divisor")

 dividend x4 - 3x2 + 4x - 3 -divisor * x2 x4 + x3 - 3x2 remainder - x3 + 4x - 3 -divisor * -x1 - x3 - x2 + 3x remainder x2 + x - 3 -divisor * x0 x2 + x - 3 remainder 0

Quotient : x2-x+1 Remainder : 0

Trying to factor by splitting the middle term

2.6Factoring x2-x+1 The first term is, x2 its coefficient is 1.The middle term is, -x its coefficient is -1.The last term, "the constant", is +1Step-1 : Multiply the coefficient of the first term by the constant 1•1=1Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -1.

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

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