Question

Create a 4-term polynomial that has (x² + 4) as one of its factors.

A) x⁴ + 4x² + 4
B) x⁴ - 4x² + 4
C) x³ + 4x
D) x³ - 4x

Answer 1

To create a 4-term polynomial with (x² + 4) as a factor, multiply (x² + 4) by another polynomial using the distributive property.

Step-by-step explanation:

To create a 4-term polynomial that has (x² + 4) as one of its factors, we need to multiply (x² + 4) by another polynomial. To do this, we can use the distributive property. We can multiply the factors of (x² + 4) with the factors of the other polynomial:

(x² + 4)(x² + a) = x²(x² + a) + 4(x² + a) = x⁴ + ax² + 4x² + 4a = x⁴ + (a + 4)x² + 4a

So, the 4-term polynomial that has (x² + 4) as one of its factors would be x⁴ + (a + 4)x² + 4a. The constant term 4a can vary depending on the value of a.