Question

if X + 1 is a factor of ax cube + 2 x square - x + 3x- 7 then what is the value of a​

Answer 1

$\sf \huge \blue {Answer}$

$\sf Since \: x+1 \: is \: a \: factor \: of \: the \: polynomial \: p(x) = ax³ + 2x² - x + 3x - 7$

$\sf Therefore, \: by \: Factor \: theorem \: p(-1) = 0$

$\sf p(-1) = a(-1)³ + 2(-1)² -(-1) +3(-1) - 7$

$\sf 0 = -a + 2 + 1 - 3 - 7$

$\sf 0 = -a - 7$

$\sf \boxed{a = -7}$

Answer 2

$\huge \red {Answer}$

$As, \: x+1 \: is \: a \: factor \: of \: the \: polynomial$ $p(x) = ax³ + 2x² - x + 3x - 7$

$Therefore, \: x=-1 \: will \: be$$the \: root \: of \: the \: polynomial$

$By \: Factor \: theorem \: we \: have \: p(-1) = 0$

$p(-1) = a(-1)³ + 2(-1)² -(-1) +3(-1) - 7$

$-a + 2 + 1 - 3 - 7 = 0$

$-a - 7 = 0$

$-a = 7$

$a = -7$

Therefore, value of a is -7.