Try to see this problem as:
ax^2 + bx + c
The first step is to find factors of c (-6) that add up to -5
2 x 3 = 6
and 1 x 6 = 6
we know that 6 -1 = 5 so that works.
These numbers would be 6 and -1, so we plug them in as b
`p^2 - p + 6p - 6`
`(p^2 - p) + (6p - 6)`
Factor out common factors:
p (p - 1 ) + 6 (p - 1)
Now set these parentheses equal to 0 and solve:
p+6 = 0
p = -6
p-1 = 0
p = 1
We can use intercept form to factor easily.
(p+1)(p-6)=0 We got this because we choose specific numbers that satisfy the conditions that the two numbers have to add up to -5 and also multiply to -6. 1+-6 equals -5 and 1*-6=-6 so the numbers that I factored are correct.
Now that we have this, we can find the solutions to the equation by moving the numbers to the right of equal sign.
The two solutions to equation are -1 and 6.
Usually for equations like this you do not need to go through the while entire steps since the leading coefficient has a 1. all you need to is the multiplies of the last in this case 6 that add up to the middle term, -5 and fill in the formula (p+/- no.)(p+/- no.) I will demonstrate.
So 6x1=6 1-6=-5
and 2x3=6 -2-3=-5
Now Here is the thing both of the multiples of 6, when added, equal -5 but there is only one right one and it's 1-6. This is the right answer because when multiplied 1x-6 will give you -6 whereas -2 x-3 will you a positive 6.
Not take 1-6 and fill in the blank
(p+1)(p-6) You can check your answer by foiling and you'll et the same answer.