Answer:
(-5p + 2)(-p + 10)
Step-by-step explanation:
-52p + 20
(-5p + 2)(-p + 10)
You can double check this by using the distributive property..
-5p * -p = -5p^2
2*-p = -2p
10*-5p = -50p
10*2 = 20
-5p^2 + -2p + -50p + 20
Now we combine like terms and simplify
-5p^2 -52p + 20
So, we are correct
To perform this check, you must use the following theorem: is a lower bound for the zeroes of
if, when divide
by
, the quotient and the remainter alternate signs.
Since the long division yields the result
You can see that the signs don't alternate (the last two terms are positive). So, -1 is not a lower bound.
In fact, the actual roots of the polynomial are -3, -2, 1, 3, so as you can see there are roots smaller than -1.