Question

divided f(x)=x^3+3x^2+3x-9 by g(x) =x-3​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

STEP

2

:

x3 - 3x2 + 3x - 9

Simplify —————————————————

x - 3

Checking for a perfect cube :

2.1 x3 - 3x2 + 3x - 9 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3 - 3x2 + 3x - 9

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

Group 1: 3x - 9

Group 2: -3x2 + x3

Pull out from each group separately :

Group 1: (x - 3) • (3)

Group 2: (x - 3) • (x2)

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Add up the two groups :

(x - 3) • (x2 + 3)

Which is the desired factorization

Polynomial Roots Calculator :

2.3 Find roots (zeroes) of : F(x) = x2 + 3

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 3.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,3

Let us test ....