Need help with the factor theorem (Unit 1)

[sondang]

Hi I'm new to this forum, im not sure if i can post questions like this but anyway here we go!
Can anyone help solve this question for me??

Find the values of a and b and factorise the polynomial P(x) = x3 + ax2 − x + b, given that
P(x) is divisible by x − 1 and x + 3.

And I was just wondering how can I improve on my extended-answer type questions as I'm struggling and I don't want to be struggling even more with these type of questions in year 12

[Mr. Study]

If P(x) = x3 + ax2 − x + b is divisible by x-1 and x+3, that would mean x-1 and x+3 are factors.

Remember when factorising an equation and solving for x, like f(x)=x^2+5x+6. The factor form of that would be (x+3)(x+2). However, if we wanted to know what values of x make f(x)=0, we can actually let x+3=0 and x+2=0 and solve for x.

Therefore the factors are x=-3 and x=-2. Let f(-3), which would equal =0 and f(-2), which would equal zero.

So for your question, you can form simultaneous equations. That is by subbing x= 1 and x=-3 and let f(1)=0 or f(-3)=0.

Hopefully that explains it, I can't really explain things well without giving an example.

[sondang]

Thanks for the quick help!!
Now I can go to bed