Question

If x-3 is a factor of the polynomial x3+4x2+kx-30 find the value of k​

Answer 1

k = -11

Explanation:

The Factor Theorem states that if (x - c) is a factor of the polynomial f(x), then f(c) = 0.

In this case, we know that (x - 3) is a factor of the polynomial f(x) = x³ + 4x² + kx - 30. Therefore, we can use the Factor Theorem to solve for k by equating f(3) to zero.

`\begin{aligned}f(3)&=0\\\implies 3^3 + 4(3^2) + 3k - 30 &= 0\\ 27 + 4(9) + 3k +33 &= 0\\27+36+3k-30&=0\\3k+33&=0\\ 3k+33-33&=-33\\3k&=-33\\3k / 3&=-33 / 3\\k&=-11\end{aligned}`

Therefore, the value of k is -11.