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if the roots are a and b then (x-a) and (x-b) are factors of the polynomial. the highest exponent of the variable is 4 so there are 4 roots. f(x) = (x-a)(x-b)(x-c)(x-d) roots a, b, c, d f(x) divided by (x-a)(x-b) = (x-c)(x-d)
can you see f(x)/x(x+2) = a quadratic to be factored ? when you factor that quadratic set = 0 solve to get the other roots
okay, I divided x^4-5x^2+2x by x-2. I got x^3+2x-x. Is that what I was supposed to do?
root -2 factor (x-(-2) = x + 2 divide yes but by x +2 other factor x
When I divide the original equation by x+2 I get a remainder. Have I just made a mistake somewhere? I will send a photo of my working out...
sorry I am blanking out what happens when you divide by x^2 + 2 ?
Oh! I havnt done that yet! Sorry let me try that now
you divide the quotient by x your constant was 8 factors of 8 are ? did not check your division remainder needed for "quadratic"
the remainder theorem says if (x-a) is a factor then there is no remainder when you compute f(a)
Yes, I know that. I just dont understand how to get the other two roots. When trying to figure out how to do it myself I looked at the answers (back of my text book) and it said the answers were -1 and plus or minus the square root of 2. How do I get to those answers? Would it be better if I sent a picture of the questions from the actual book?
sorry I can't explain it better right now when I divide f(x) by x^2 had to add 1 to complete the quadratic so x-1 is a factor Quotient x^2 - 4 the factors are (x+2)(x-2)
I guess from the method you need to use the remainder you have is -8 and one root is -2 so the other 4
Ok, thanks very much for your help, unfortunately I still dont understand but maybe its because where I am its quite late so I will look at it again in the morning when you brain is fresh :). Thank you very much though