If the polynomials 2x³ + 9x² + 3x – 5 and x³ + x² - 4x + a leave the same remainder when divided by x-2, find the value of a.

If the polynomials 2x³ + 9x² + 3x – 5 and x³ + x² - 4x + a leave

1.	If the polynomials 2x³ + 9x² + 3x – 5 and x³ + x² - 4x + a leave the same remainder when divided by x-2, find the value of a.
Answer» <html><body><p>-step <a href="https://interviewquestions.tuteehub.com/tag/explanation-455162" style="font-weight:bold;" target="_blank" title="Click to know more about EXPLANATION">EXPLANATION</a>:Let the given polynomials be f(x) and <a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a>(x).When f(x) and g(x) are divided by (x-2) they leave the same remainder.I.e (x-2) is a <a href="https://interviewquestions.tuteehub.com/tag/factor-458892" style="font-weight:bold;" target="_blank" title="Click to know more about FACTOR">FACTOR</a> of f(x) and g(x). It <a href="https://interviewquestions.tuteehub.com/tag/means-1091780" style="font-weight:bold;" target="_blank" title="Click to know more about MEANS">MEANS</a> 2 is the zero of f(x) and g(x)So that,f(2) = g(2)2x³+ax²+3x-5 = x³+x²-4x+a2(2)³+a(2)²+3(2)-5 = 2³+2²-4(2)+a2(<a href="https://interviewquestions.tuteehub.com/tag/8-336412" style="font-weight:bold;" target="_blank" title="Click to know more about 8">8</a>)+a(4)+6-5 = 8+4-8+a16+4a+1 = 4+a17+4a = 4+a4a-a = 4-173a = -13a = -13/3.Was this answer helpful</p></body></html>