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
