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If (x+1) is a factor of x³ + 2x² - 5x - 6, find the other factors using long division.​

Answer» <html><body><p><strong><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a>:</strong></p><p>Let <a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a>(x)=x </p><p>3</p><p> −2x </p><p>2</p><p> −5x+6</p><p>⇒f(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)=1 </p><p>3</p><p> −21 </p><p>2</p><p> −5×1+6=1−2−5+6=0</p><p>Using synthetic <a href="https://interviewquestions.tuteehub.com/tag/division-957437" style="font-weight:bold;" target="_blank" title="Click to know more about DIVISION">DIVISION</a>, we have</p><p>x </p><p>2</p><p> −x−6=0 is the other <a href="https://interviewquestions.tuteehub.com/tag/factor-458892" style="font-weight:bold;" target="_blank" title="Click to know more about FACTOR">FACTOR</a></p><p>(x−1)(x </p><p>2</p><p> −x−6)=0</p><p>=(x−1)(x </p><p>2</p><p> −3x+2x−6)=0</p><p>=(x−1)(x(x−3)+2(x−3))=0</p><p>=(x−1)(x+2)(x−3) are the factors of f(x)</p><p></p></body></html>


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