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Factor Theorem

I'll post the question below i thought it meant divide by (x-1) after i proved it 1 was a factor but i can't do it.
Thanks for any help

Just substitute in 1 into the equation and if it equals to zero then that means (x-1) is a factor

Reply 3

T!gger34

There are 3 ways forward, one of which never seems to be used nowadays for some reason, so I'll not bother describing it even though it is absurdly easy!
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One is to perform the long division x-1) x^3 + 0x^2 - 7x +6 ,

The other is to do it by inspection (x-1)(ax^2 + bx + c)

Reply 4

A0W0N

Original post by sam72016

Just substitute in 1 into the equation and if it equals to zero then that means (x-1) is a factor

Yes I've done that its the second part that i don't understand

Reply 5

mqb2766

Original post by A0W0N

Yes I've done that its the second part that i don't understand

The correct explanation is to divide the cubic by (x-1). Really, you have a factor, then a simple inspection is enough
x^3 - 7x + 6 = (x-1)*quadratic
The quadratic and constant terms are obvious? Linear term isn't much more difficult.

Then factorize the quadratic, to get the two other solutions.