Question

best is brainly full explanation
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Answer 1

Step-by-step explanation:

$p(x) = 2 {x}^{3} + b {x}^{2} + 3x - 5$

$q(x) = {x}^{3} + {x}^{2} - 4x - b$

by remainder theorem remainder left when a linear polynomial x-a is divided by p(x) is p(a)

so when p(x) and q(x) are divided by x-2 the remainder left is p(2) and q(2) respectively

$p(2) = 2( {2}^{3} ) + b({2)}^{2} + 3(2) - 5 = 16 + 4b + 6 - 5 = 4b + 17$

---------(1)

$q(2) = {2}^{3} + {2}^{2} - 4(2) - b = 8 + 4 - 8 - b = 4 - b$

------------(2)

it is given that both the polynomials leave same remainder so

4b+17=4-b

5b=-13

b= -13/5

hence we have got the value of b as -13/5

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