Question

if x minus 2 is a factor of 2 x cube - 11 X square +a X - 6 then find the value of a​

Answer 1

as

$x - 2$

is a factor

then

$x = 2$

so

$p(x) = 2 {x}^{3} - 11 {x}^{2} + ax - 6$

now

$p(2) = 2 {(2)}^{3} - 11 {(2)}^{2} +2 a - 6$

now after simplifying we get

$- 34 + 2a$

but we have 2 as a factor then this equation is equal to zero so

$- 34 + 2a = 0$

now

$2a = 34$

again after simplifying

$a = 17$

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