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

Equation at the end of step 1 : Step 2 : Equation at the end of step 2 : Step 3 : 3w3 + 7w2 - 4w + 3 Simplify / w + 3 Checking for a perfect cube:

3.1 3w3 + 7w2 - 4w + 3 is not a perfect cube

Trying to factor by pulling out:

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