Question

answer this question​

Answer 1

Step-by-step explanation:

$let \: the \: given \: polynomial \: be \: p(x) \: and \: g(x)$

$when \: p(x) \: and \: g(x) \: are \: divided \: by \: (x - 2) \: they \: leave \: the \: same \: remainder$

$i.e \: (x - 2) \: is \: a \: factor \: of \: p(x) \: and \: g(x)$

$it \: means \: 2 \: is \: the \: zero \: of \: p(x) \: and \: g(x)$

$so \: that$

$p(2) = g(2)$

$2( {2})^{3} + b( {2})^{2} + 3( {2})^{2} - 5 = {2}^{3} + {2}^{2} - 4(2) + b$

$16 + 4b + 1 = 4 + b$

$17 + 4b = 4 + b$

$4b - b = 4 - 17$

$3b = - 13$

$b = \frac{ - 13}{3}$