Question

3x^3-5x^2+2x-11 for x=3
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Answer 1

Answer:

x3) - 5x2) + 3x) - 11

STEP

2

:

Checking for a perfect cube

2.1 x3-5x2+3x-11 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-5x2+3x-11

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

Group 1: 3x-11

Group 2: x3-5x2

Pull out from each group separately :

Group 1: (3x-11) • (1)

Group 2: (x-5) • (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) = x3-5x2+3x-11

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 -11.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,11

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -20.00

-11 1 -11.00 -1980.00

1 1 1.00 -12.00

11 1 11.00 748.00

Polynomial Roots Calculator found no rational roots

Final result :

x3 - 5x2 + 3x - 11

Answer 2

$3 {x}^{3} - 5 {x}^{2} + 2x - 11$

If x= 3;

$3 {(3)}^{3} - 5 {(3)}^{2} + 2(3) - 11$

$3(27) - 5(9) + 6 - 11$

$81 - 45 - 5$

$31$