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you could write everything on one side and try to factor
x^4+x^3=4x^2+4x x^4 + x^3 - 4x^2 - 4x = 0 take out the common factor x x(x^3 + x^2 - 4x - 4) = 0 so what is one root?
when two expression are multiplied and the result is zero then either one = zero right?
yes, so it would be D?
dont jump to conclusions all we can say is that x = 0 one root is 0
- so it could be any of the 4 options now we can look to see if we can factor the cubic in the parentheses
x^3 + x^2 - 4x - 4 = 0
we can factor this by grouping can you factor the first 2 terms x ^3 and x^2 - what is the highest common factor of these 2?
what is the highest thing which divides into x^3 and x^2?
is it x or is it x^2?
it would be x^2
yes so it factors to x^2(x + 1) OK with that?
right so so far we have x^1(x + 1) - 4x - 4 = 0 it would be nice if we could get another (x + 1) so we could factor further and we can do this by taking out -4 from the lat 2 terms so we get x^2( x + 1) - 4(x + 1) = 0 taking out the x+ 1 (x^2 - 4)(x + 1) = 0 do you follow that ok?
sure do :)
great so now we have x^2 - 4 = 0 and x + 1 = 0 x = 2 , -2 and -1 so final answer is 2, -2, -1 and 0
A is correct
Thank you for explaining this to me!!!
its always worth checking to see if you can factor by grouping
you cant always do it of course