Get an answer in 5 minutes Ask a question to our educators
MATHS

# For what values of b is (x-b) a factor of 3x^3 +(b+3)x^2 -(4b^2 +b-7)x-4?

Let f(x) = 3x^3 + (b+3)x^2 - (4b^2+b-7)x-4 Then (x-b) is a factor of f(x) if and only if f(b)=0, because if (x-b) is a factor of f(x) then we can write f(x)=(x-b)g(x) for some other (quadratic) polynomial g, which when evaluated at b clearly equals zero. Hence we have that (x-b) is a factor of f, if and only if: 3b^3 + (b+3)b^2 - (4b^2+b-7)b-4=0 That is, if: 2b^2+7b-4=0 (2b-1)(b+4)=0 So b=-4 or 1/2  Sam Georgiou
·

284 students helped

## Similar Maths questions

Maths

Find 7s-2t when S=4 and t=-4

## What is Q&A on Scoodle?

At Scoodle we understand that everyone learns in a different way. Some people learn through practice, using essays and notes; others prefer video lessons to watch and learn, some just need help with a specifically hard question, while some learn best 1-on-1 tutoring sessions. At Scoodle we cater for all types of learning styles and needs. From GCSE Maths video lessons to A-level English essays and specialist educators in every subject - we’ve got you covered.   Scoodle has helped over 131,000 students so far

Need help with Maths?

Getting expert help from a tutor is a great way to improve your Maths grades.

## Discover learning resources by tutors

Learn Maths with Video Lessons