How does the remainder theorem allow for zeros of a polynomial to be identified?

If substituting a given number a into the polynomial results in a value of zero, then the remainder theorem states that dividing the polynomial by (x - a) gives a remainder of zero. This implies that x = a is one of the zeros of the polynomial. Having identified (x - a) as a factor of the polynomial (since it leaves a remainder of zero), we can then divide the polynomial to reduce its degree and make it easier to find any further zeros.

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.