Both formats are the same. You can extract one negative sign each from your answers to get the given solution. And the two negative signs cancel out anyway.

Or we introduce two negatives.

(-4p + 1) (3p + 1)
= [- (-4p + 1)] [- (3p + 1)]
= (4p - 1) (-3p - 1)

Thank you @Eric Nicholas K

Note that its mathematically the same, but since the question was to factorise, and you can factorise out, -1, you would lose 1 mark in exams for your current answer.

Oh I see. Thank you @Arbold K H Tan!!

Both formats are actually fine (I would not deduct marks for it) since the main goal of the term “factorise” is to reduce the quadratic expression into a product of two linear expressions. But somehow, too many negative signs do not appeal to my eye at all.

This is why I prefer (-4p + 1) (3p + 1) over (4p - 1) (-3p - 1). Because there are too many negative signs in the expression (4p - 1) (-3p - 1).

Oh ok!! Thank you so much @Eric Nicholas K

Arnold is correct.

Ir would actually actually be better if you have left it as (1 - 4p)(3p + 1). The rule of thumb is to not leave negative signs if front if possible

By far the best presentation of the possible formats is

(1 - 4p) (1 + 3p)

Not really. It depends on what you are given for the expanded form.

(1 - 4p)(1 + 3p) is only more intuitive here because the act of expansion is in flow with the given expression.

(Left term x left term
Left term x right term
Right term x left term
Right term x right term)

(1 - 4p)(1 + 3p)

= 1 + 3p - 4p - 4p(3p)

= 1 - p - 12p²

if the expression was given as -12p² - p + 1 instead, then (-4p + 1)(3p + 1) would be more intuitive. And that is probably why the answer scheme put it as such since they expect the student to rearrange in order of x² being the first, then in descending powers)

Erica, what I would recommend is to take out the negative sign from the coefficient in x² first. Makes things easier to visualise.

1 - p - 12p²

= -(12p² + p - 1)

= -(4p - 1)(3p + 1)

= (1 - 4p)(3p + 1)

Once you get the hang of it, these are easy to do mentally and we won't even have to use any cross or box method anymore.

Ok! Thank you so much @J for the advice