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If (x−3) and (x+4)(x−3) and (x+4)  are factors of polynomial P(x)P(x) , then​

Answer» <html><body><p>k me as brain listpls mark me as brain listStep-by-step explanation:Let us assume x+3=0 Then, x=−3 Given, <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  3 +ax  2 –bx+24 Now, substitute the value of x in f(x), f(−3)=(−3)  3 +a(−3)  2 –b(−3)+24 =−27+9a+3b+24 =9a+3b–3 Dividing all terms by 3 we get, =3a+b–1 From the question, (x+3) is a factor of x  3 +ax  2 –bx+24. Therefore, remainder is 0. f(x)=0 3a+b–1=0 3a+b=1 … [equation (i)] Now, assume x–4=0 Then, x=4 Given, f(x)=x  3 +ax  2 –bx+24 Now, substitute the value of x in f(x), f(4)=43+a(4)  2 –b(4)+24 =64+16a–4b+24 =88+16a–4b Dividing all terms by 4 we get, =22+4a–b From the question, (x–4) is a factor of x  3 +ax  2 –bx+24. Therefore, remainder is 0. f(x)=0 22+4a–b=0 4a–b=–22 … [equation (ii)] Now, <a href="https://interviewquestions.tuteehub.com/tag/adding-2399902" style="font-weight:bold;" target="_blank" title="Click to know more about ADDING">ADDING</a> both equation (i) and equation (ii) we get, (3a+b)+(4a–b)=1–22 3a+b+4a–b=–21 7a=–21 a=−21/7 a=−3 <a href="https://interviewquestions.tuteehub.com/tag/consider-2017521" style="font-weight:bold;" target="_blank" title="Click to know more about CONSIDER">CONSIDER</a> the equation (i) to find out ‘b’. 3a+b=1 3(−3)+b=1 −9+b=1 b=1+9 b=10 Therefore, value of a=−3 and b=10. Then, by <a href="https://interviewquestions.tuteehub.com/tag/substituting-1231652" style="font-weight:bold;" target="_blank" title="Click to know more about SUBSTITUTING">SUBSTITUTING</a> the value of a and bf(x)=x  3 –3x  2 –10x+24 (x+3)(x–4) =x(x–4)+3(x–4) =x2–4x+3x–12 =x  2 –x–12 Dividing f(x) by x  2 –x–12 we get, Therefore, x  3 –3x2–10x+24=(x2–x–12)(x–2) =(x+3)(x–4)(x–2)</p></body></html>


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