Question

If the polynomial 2x4 + kx3 + 2x2 +x -15 is a multiple of (x – 3), then find the value of k

Answer 1

put x = 3 in the polynomial,and equate it to zero
$2( {3)}^{4} + k {(3)}^{3} + 2( {3)}^{2} + 3 - 15 = 0 \\ 2 \times 81 + 27k + 18 + 3 - 15 = 0 \\ 27k + 162 + 21 - 15 = 0 \\ 27k + 183 - 15 = 0 \\27k + 168 = 0 \\ k = \frac{ - 168}{27} \\ k = - 6.22$