<span>Equation at the end of step 1 :</span><span>
<span> Step 2 :</span></span><span>Equation at the end of step 2 :</span>
<span> Step 3 :</span><span> 3w3 + 7w2 - 4w + 3
Simplify / w + 3
</span>Checking for a perfect cube :
<span> 3.1 </span> <span> 3w3 + 7w2 - 4w + 3</span> is not a perfect cube
Trying to factor by pulling out :
<span> 3.2 </span> Factoring: <span> 3w3 + 7w2 - 4w + 3</span>
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -4w + 3
Group 2: <span> 3w3 + 7w2</span>
Pull out from each group separately :
Group 1: (-4w + 3) • (1) = (4w - 3) • (-1)
Group 2: <span> (3w + 7) • (w2)</span>
<span>Bad news !! Factoring by pulling out fails :
</span>The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
<span> 3.3 </span> Find roots (zeroes) of : <span> F(w) = 3w3 + 7w2 - 4w + 3</span>
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 <span> 3.
</span>The factor(s) are:
of the Leading Coefficient : <span> 1,3
</span>of the Trailing Constant : <span> 1 ,3
</span>Let us test ....
<span><span> P Q P/Q F(P/Q) Divisor</span><span> -1 1 -1.00 11.00 </span><span> -1 3 -0.33 5.00 </span><span> -3 1 -3.00 -3.00 </span><span> 1 1 1.00 9.00 </span><span> 1 3 0.33 2.56 </span><span> 3 1 3.00 135.00 </span></span>
Polynomial Roots Calculator found no rational roots
Polynomial Long Division :
<span> 3.4 </span> Polynomial Long Division
Dividing : <span> <span>3w3 + 7w2 - 4w + 3</span>
("Dividend")
</span> By : <span> w + 3 ("Divisor")
</span>
<span><span>dividend <span> 3w3 </span>+<span> 7w2 </span>- 4w + 3 </span><span>- divisor<span> <span>* 3w2</span> </span> <span> 3w3 </span>+<span> 9w2 </span> </span><span>remainder -<span> 2w2 </span>- 4w + 3 </span><span>- divisor<span> <span>* -2w1</span> </span> -<span> 2w2 </span>- 6w </span><span>remainder 2w + 3 </span><span>- divisor<span> <span>* 2w0</span> </span> 2w + 6 </span><span>remainder - 3 </span></span>
Quotient : <span> <span>3w2 - 2w + 2</span>
</span> Remainder : <span> -3
</span>
Final result :<span> 3w3 + 7w2 - 4w + 3 over w + 3
</span>
