Question

1)Find the remainder when x3 – 3x2 +2x -5 is divided by (x-3)

Answer 1

Step-by-step explanation:

(x3-3x2+2x-5)/(x-3)

Final result :

x2 - 2x + 2

Step by step solution :

Step 1 :

Equation at the end of step 1 :

Step 2 :

x3 - 3x2 + 4x - 2

Simplify —————————————————

x - 1

Checking for a perfect cube :

2.1 x3 - 3x2 + 4x - 2 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3 - 3x2 + 4x - 2

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

Group 1: 4x - 2

Group 2: x3 - 3x2

Pull out from each group separately :

Group 1: (2x - 1) • (2)

Group 2: (x - 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) = x3 - 3x2 + 4x - 2

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 1 and the Trailing Constant is -2.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2