<em>Answer:</em>
<em></em>
<em> 2x3 - 5x2 + 2x - 7</em>
<em> ——————————————————</em>
<em> x - 2 </em>
<em>Step-by-step explanation: 2x3 - 5x2 + 2x - 7</em>
<em> Simplify ——————————————————</em>
<em> x - 2 </em>
<em>Checking for a perfect cube :</em>
<em> 3.1 2x3 - 5x2 + 2x - 7 is not a perfect cube</em>
<em></em>
<em>Trying to factor by pulling out :</em>
<em> 3.2 Factoring: 2x3 - 5x2 + 2x - 7 </em>
<em></em>
<em>Thoughtfully split the expression at hand into groups, each group having two terms :</em>
<em></em>
<em>Group 1: 2x - 7 </em>
<em>Group 2: 2x3 - 5x2 </em>
<em></em>
<em>Pull out from each group separately :</em>
<em></em>
<em>Group 1: (2x - 7) • (1)</em>
<em>Group 2: (2x - 5) • (x2)</em>
<em></em>
<em>Bad news !! Factoring by pulling out fails :</em>
<em></em>
<em>The groups have no common factor and can not be added up to form a multiplication.</em>
<em></em>
<em>Polynomial Roots Calculator :</em>
<em> 3.3 Find roots (zeroes) of : F(x) = 2x3 - 5x2 + 2x - 7</em>
<em>Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0 </em>
<em></em>
<em>Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers</em>
<em></em>
<em>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</em>
<em></em>
<em>In this case, the Leading Coefficient is 2 and the Trailing Constant is -7.</em>
<em></em>
<em> The factor(s) are:</em>
<em></em>
<em>of the Leading Coefficient : 1,2</em>
<em> of the Trailing Constant : 1 ,7</em>
<em></em>
<em> Let us test ....</em>
<em></em>
<em> P Q P/Q F(P/Q) Divisor</em>
<em> -1 1 -1.00 -16.00 </em>
<em> -1 2 -0.50 -9.50 </em>
<em> -7 1 -7.00 -952.00 </em>
<em> -7 2 -3.50 -161.00 </em>
<em> 1 1 1.00 -8.00 </em>
<em> 1 2 0.50 -7.00 </em>
<em> 7 1 7.00 448.00 </em>
<em> 7 2 3.50 24.50 </em>
<em></em>
<em>Polynomial Roots Calculator found no rational roots</em>
<em></em>
<em>Polynomial Long Division :</em>
<em> 3.4 Polynomial Long Division</em>
<em>Dividing : 2x3 - 5x2 + 2x - 7 </em>
<em> ("Dividend")</em>
<em>By : x - 2 ("Divisor")</em>
<em></em>
<em>dividend 2x3 - 5x2 + 2x - 7 </em>
<em>- divisor * 2x2 2x3 - 4x2 </em>
<em>remainder - x2 + 2x - 7 </em>
<em>- divisor * -x1 - x2 + 2x </em>
<em>remainder - 7 </em>
<em>- divisor * 0x0 </em>
<em>remainder - 7 </em>
<em>Quotient : 2x2 - x </em>
<em>Remainder : -7 </em>
<em></em>
<em>so x=-7</em>
<em></em>