Question

Simplify the following:

Answer 1

Answer:

3x3 + 4x2 + 9x + 28

Step-by-step explanation:

Step by Step Solution

More Icon

STEP

1

:

Equation at the end of step 1

(((3 • (x3)) + 22x2) + 9x) + 28

STEP

2

:

Equation at the end of step

2

:

((3x3 + 22x2) + 9x) + 28

STEP

3

:

Checking for a perfect cube

3.1 3x3+4x2+9x+28 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 3x3+4x2+9x+28

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

Group 1: 9x+28

Group 2: 3x3+4x2

Pull out from each group separately :

Group 1: (9x+28) • (1)

Group 2: (3x+4) • (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 :

3.3 Find roots (zeroes) of : F(x) = 3x3+4x2+9x+28

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 3 and the Trailing Constant is 28.

The factor(s) are:

of the Leading Coefficient : 1,3

of the Trailing Constant : 1 ,2 ,4 ,7 ,14 ,28

Let us test ....

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

-1 1 -1.00 20.00

-1 3 -0.33 25.33

-2 1 -2.00 2.00

-2 3 -0.67 22.89

-4 1 -4.00 -136.00

Note - For tidiness, printing of 19 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

3x3 + 4x2 + 9x + 28