Question

If 2x³-kx²+5x+2 is exactly divisible by (x+2) then, k=-6​

Answer 1

$k = - 6 \\ g(x) = x + 2 \\ x + 2 = 0 \\ x = - 2 \\ f(x) = {2x}^{3} - k {x}^{2} + 5x + 2 \\ f( - 2) = 2 {( - 2)}^{3} - ( - 6)( - 2) + 5( - 2) + 2 \\ f( - 2) = 2 \times (- 8) - (12) + ( - 10) + 2 \\ f( - 2) = - 16 - 12 - 10 + 2 \\ f( - 2) = - 38 + 2 \\ f( - 2) = - 36$

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Answer 2

$\huge\mathcal{\fcolorbox{aqua}{green}{\fcolorbox{aqua}{orange}{\:\:\:\:ᴀ᭄nswer}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: g(x) = x + 2$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 2 = 0$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\red{x = - 2}}$

$\: \: p(x) = 2 {x}^{3} - k {x}^{2} + 5x + 2$

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

$= >( 2 \times - 8) - (k \times 4) - 10 + 2 = 0$

$= > - 16 - 4k - 8 = 0$

$= > - 4k - 24 = 0$

$= > - 4k = 24$

$= > \boxed {\pink{ k = - 6}}$

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