What are the steps to (3w^3+7^2-4w+3) and (w+3)

3.2 Factoring: 3w3 + 7w2 - 4w + 3

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

Group 1: -4w + 3
Group 2: 3w3 + 7w2

Pull out from each group separately :

Group 1: (-4w + 3) • (1) = (4w - 3) • (-1)
Group 2: (3w + 7) • (w2)

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(w) = 3w3 + 7w2 - 4w + 3
Polynomial Roots Calculator is a set of methods aimed at finding values of  w  for which   F(w)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers w 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 3.

The factor(s) are:

of the Leading Coefficient : 1,3
of the Trailing Constant : 1 ,3

Let us test ....

P Q P/Q F(P/Q) Divisor -1 1 -1.00 11.00 -1 3 -0.33 5.00 -3 1 -3.00 -3.00 1 1 1.00 9.00 1 3 0.33 2.56 3 1 3.00 135.00

Polynomial Roots Calculator found no rational roots

Polynomial Long Division :

3.4    Polynomial Long Division
Dividing : 3w3 + 7w2 - 4w + 3
                              ("Dividend")
By         :    w + 3    ("Divisor")

dividend 3w3 + 7w2 - 4w + 3 - divisor * 3w2 3w3 + 9w2 remainder - 2w2 - 4w + 3 - divisor * -2w1 - 2w2 - 6w remainder 2w + 3 - divisor * 2w0 2w + 6 remainder - 3

Quotient : 3w2 - 2w + 2
Remainder : -3

Final result : 3w3 + 7w2 - 4w + 3 over w + 3