Question

If p-1 is a factor of p⁴+p²+p-k what is the value of k

Answer 1

Answer:

k = 3

Step-by-step explanation:

If p-1 is a factor of p⁴+p²+p-k, then we can express the polynomial in form

p⁴+p²+p-k = (p-1) * (ap³ + bp² + cp + d)

where a,b,c,d are constants. The important thing is that we can subst in p = 1 to make the polynomial zero. We can do this for original polynomial. WE must have to equal to 0 when we use p = 1 substitution...

1⁴+1²+1-k = 0

3 - k = 0

k = 3