POLYNOMIALS

I'm really sorry, i'm preparing for O levels, so i have a lot of maths questions to ask... please excuse me...

Question:

Find the value of k for which a-3b is a factor of a^4 - 7a^2b^2 + kb^4. Hence, factorise completely.

How do i even find k???


Please help thankyou!

asked by Aoi
  1. Using either long division or by synthetic division I go

    (a^4 - 7a^2b^2 + kb^4)÷ (a-3b) = a^3 + 3a^2b - 7ab^2 + 21b^3 with a remainder of 63k^4 + kb^4

    but there was to be no remainder, so
    63k^4 + kb^4 = 0
    k = -63

    so a^3 + 3a^2b - 7ab^2 + 21b^3 = 0
    use grouping
    a^2(a+3b) + 7b^2(a+3b) = 0
    (a+3b)(a^2 + 7b) = 0

    so the original factors to
    (a-3b)(a+3b)(a^2 + 7b)

    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Criminal Justice

    I am preparing the DSST (Dantes) examine in Criminal Justice. I had been looking for some practice tests for this examine. The only practice examines I could locate werei in "Rudman's Quesiton & Answers on the Dantes Subject
  2. Calculus - Maths

    I got a few questions. Hope ya'll can help out. 1) for F(X) = 6x - 2x^2 Find the gradient of the chord joining the point where the X coorinates are 1 and (1+h) respectively. b) hence find the gradient at x=1 2) Find the
  3. Education

    Bloom's taxonomy levels A) correspond directly to grade levels in constructing an action plan. B) help teachers to gauge the cognitive levels required for their objectives. C) identify at which step in the DID cycle instruction is
  4. MAths algebra

    A diagonal of a square parking lot is 75 meters.Find to the nearest meter, the length of a side of a lot
  5. statistics

    What SPECIFIC statistical test would be applied to these data collected to answer the following questions? What’s the average amount of pain Mr. Smith reported yesterday? Is there a significant difference in depression levels
  6. General question

    Hi. Is there any ways that I can post the questions up here using pictures? As some of the questions requires diagrams to be solved. Thanks a lot.
  7. Science - Please Check

    Suppose that the local temperature changes in favor of greater oxygen levels in the water. Write a short paragraph to describe how both the population of the small fish species and wading bird population would change in response
  8. Maths - More than one question please help me

    Hi everyone :) I need a lot of help. I have many questions i don't get how to do and even if you can help me with one of them, I'd truly appreciate it. I really need the help and i gotta hand this in soon so please help if you
  9. acct. correction

    can someone correct these for me thanks. for the accounting cycle. i have to place these in order. a) Posting the journal entries b) Journalizing and posting adjusting entries c) Preparing the adjusted trial balances d)
  10. Ms. Sue

    I've looked at a lot of these questions and I'm disappointed that people don't appreciate Ms. Sue at all. She takes a lot of time out of her day to help students get better grades. Thanks Ms. Sue, for being a great tutor.

More Similar Questions