Question

What should be subtracted from p(x) = x⁴ + 85 so that the resulting polynomial is divisible by x + 3 ?

Answer 1

Answer:

166 is subtracted from p(x) = x⁴ + 85 so that the resulting polynomial is divisible by x + 3.

Step-by-step explanation:

Given: p(x) = x⁴ + 85

What should be subtracted from p(x) = x⁴ + 85 so that the resulting polynomial is divisible by x + 3.

Put x = -3

p(x) = x⁴ + 85

= (-3)⁴ + 85

= 81 + 85

= 166

So, 166 is subtracted from p(x) = x⁴ + 85 so that the resulting polynomial is divisible by x + 3.

Answer 2

Answer:

As a result, 166 is subtracted from p(x) = x4 + 85, resulting in a polynomial divisible by x + 3.

Step-by-step explanation:

In accordance with the information provided in the question,

Given the data in question  subtracted from p(x) = x⁴ + 85 so that the resulting polynomial is divisible by x + 3

As we get,

$p(x)=x^{4} +85$

We have put the value in above question x=-3

So,

$p(x)=x^{4} +85$

=$(-3)^{4} +85\\=81+85\\=166$

As a result, 166 is subtracted from p(x) = x4 + 85, resulting in a polynomial divisible by x + 3.