### (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-1 | 1 | -1.00 | -9.00 | ||||||

-3 | 1 | -3.00 | 39.00 | ||||||

1 | 1 | 1.00 | -1.00 | ||||||

3 | 1 | 3.00 | 63.00 |

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term2.4Factoring 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 term2.6Factoring 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