X^2 + 4X + 6 is a factor of X^4 + rX^2 + s

Name: Katie
Who is asking: Student
Level of the question: Secondary

Question: Hello !
I hope someone could answer this question; i have been struggling to get the right answer.

the question is : If X² + 4X + 6 is a factor of X⁴ + rX² + s, then find the value of r+s?

thanks alot

Katie,

When your textbook say that X² + 4X + 6 is a factor of X⁴ + rX² + s I think the authors mean that there are numbers a and b so that

X⁴ + rX² + s = (X² + 4X + 6)(X² + aX + b)

Expand the right side and then the right and left sides should be identical polynomials.

Steve and Penny