Question

polynomial x cube + x square + bx - 20 when divided by x minus 5 and x minus 3 leaves remainder 0 and minus 2 find a and b

Answer 1

Here is your solution,

p(x) = x³+x²+bx-20

g(x) = x-5 and x-3

r(x) = 0 and -2

x-5 = 0

x = 5

p(5) = (5)³ + (5)² + b×5 - 20

= 125 + 25 + 5b - 20

= 130 +5b = 0

= 5b = -130

= b = -130/5

= b = -26

x-3 = 0

x = 3

p(x) = (3)³+(3)²+b×3-20

= 27+9+3b-20

= 16+3b = -2

= 3b = -2-16

= 3b = -18

= b = -18/3

= b = -6

So, values of b are -26 and -6.

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Sorry for late answer.