Question

the polynomials ax³+3x²-3 and 2x³-5x+a when divided by (x-4) leaves remainders R1 and R2 respectively. find the value of a if R1=R2

Answer 1

By using remainder theorem ,

x - 4 = 0

x = 4


fill value of x in each equation to find the remainder ,
ax³ + 3x² - 3

= a(4)³ + 3(4)² - 3

= a(64) + 3(16) - 3

= 64a + 48 - 3

= 64a + 45

let take that ,
R1 = 64a + 45



2x³ - 5x + a

= 2(4)³ - 5(4) + a

= 2(64) - 20 + a

= 128 - 20 + a

= 108 + a

let take that ,
R2 = 108 + a

if ,
R1 = R2

64a + 45 = 108 + a

64a - a = 108 - 45

63a = 63

a = 63/63

a = 1

so, value of a is "1"

Answer 2

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