Question

f the polynomial
8
x
3
+
k
x
2
+
16
x
−
16
leaves a remainder of
−
1296
when divided by
x
+
5
, find the value of
k
.

Answer 1

Answer

$k = 95.68$

Step by step explanation l.

$f(x) = 8 {x}^{3} +k {x}^{2} + 16x - 16 \\ \\ given \\ \\ f( - 5) = 1296 \\ \\ 8 {( - 5)}^{3} + k {( - 5)}^{2} + 16( - 5) - 16 = 1296 \\ \\ - 1000 + 25 {k} - 80 - 16 = 1296 \\ \\ 25 {k}^{2} = 2392 \\ \\ k = 95.68$

Hope it helps