<span> 3.1 </span> <span> 3w3 + 7w2 - 4w + 3</span> is not a perfect cube
<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.
<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 ....
Polynomial Roots Calculator found no rational roots
<span> 3.4 </span> Polynomial Long Division
Dividing : <span> <span>3w3 + 7w2 - 4w + 3</span>
("Dividend")
</span> By : <span> w + 3 ("Divisor")
</span>
Quotient : <span> <span>3w2 - 2w + 2</span>
</span> Remainder : <span> -3
</span>