7y³ + y² - 8y
First you can take out a factor of 'y' :
7y³ + y² - 8y = y(7y² + y - 8)
Now you need to think about multiplies of 7 and multiplies of 8:
7 = 7×1
8 = 8×1 = 4×2
So if you look at these and try out which multiplies work best you can see that we need to use: 7×1 and 8×(-1)
So,
y(7y² + y - 8) = y(7y + 8)(y - 1) This is the final answer.
You can check that this is correct by multiplying it out:
y(7y + 8)(y - 1) = y(7y² - 7y + 8y - 8) = y(7y² + y - 8) = 7y³ + y² - 8y
⇒ which is the original answer