What divisor is represented by the synthetic division below?

The divisor represented by the given synthetic division is;

Option C; x + 5

Synthetic division is simply a shortcut in polynomial division used to get the zeros of that polynomial.

Let us say we have a polynomial with the function;

y = x² + 5x + 6

Let us say we want to test if (x - 1) is a factor of the polynomial

This means, x - 1 = 0 and x = 1 is a zero of the polynomial.

Now, in synthetic long division, if we want to divide the function x² + 5x + 6 by  x - 1,

what it means is that the numbers inside the division box will only be the leading coefficients of the given polynomial while the number outside will be the supposed zero of the polynomial we want to check which in this case is 1. The leading coefficients are; 1, 5 and 6. Thus, our synthetic division would be like;

      1  I  1    5    6

         I

From the above we can see that the divisor was 1 which was from a factor of the polynomial (x - 1)

Applying that to our question means that -5 is the divisor and it is from the factor; (x + 5)

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