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Question

20,21 and question 22

​Q20. Find the values of a it x3 – 5x (a – 1) – 3(x + 1) + 5a is divisible by x – a.

Q21. Find the value of a if x – a is a factor of the polynomial x5 – a x4 + x3 –a x2 + 2x + 3a – 2.

Q22. Find th remainder when x3 + 3px + q is divided by (x2 –a2) without actual division.

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Solution

Dear student
Que 21Since x-a is a factor of x5-ax4+x3-ax2+2x+3a-2=f(x) {let}so,f(a)=0a5-aa4+a3-aa2+2a+3a-2=0a5-a5+a3-a3+5a-2=05a-2=05a=2a=25
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