Question
If the polynomial (2x3 + ax2 +
3x-5) and (x3 + ax² - 2x + a) leave the same remainder when divided by (x - 2), find the remainder.Solution
To find the remainder when the polynomials (2x³ + ax² + 3x - 5) and (x3+x²-2x+a) are divided by (x - 2): 1. Evaluate the polynomials at x – 2 =0 x=2 For P(x) = 2x³ + ax2 + 3x – 5, P (2) = 2(23) +a (22) +3(2)-5 =16+4a+6-5 = 17 + 4a For Q(x) = (x3 +x²-2x+a) Q (2) =23+22 - 2(2) +a =8+4-4+a =8+a Set the remainders equal- 17+4a=8+ a Then- 3a =-9 a = -3 put a =-3 in Q (2) =8+(-3) =5
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