Question

For what value of k,is the polynomial p(x)= 3x4 – 9x3 + x2 - 15x + k completely divisible by 3x2 - 5​

Answer 1

k = -10

Explanation:

`p(x)=3x^(4) - 9x^(3) + x^(2) + 15x + k\\3x^(2) (x^(2) -3x + y) -5 (x^(2) -3x + y)`

When we expand the above

`p(x)=3x^(4) - 9x^(3) + 3x^(2)y- 5x^(2) + 15x - 5y`

When we take consider
`x^(2)` with the original expression

3y - 5 = 1

3y = 6 ⇒ y = 2

k = -5y ⇒ k = -10